In addition to the lack of evidence cited in the last post, two other issues stomp on my hypotheses about horns and take their lunch money, preventing them from explaining Mormon horns: timing and inspecificity.
Mormon horns come too early to be inspired by polygamy or Danites or the like and too late to have any claim to uniqueness. 1836—the year of the first Mormon horns I’ve identified—came and went before public polygamy (1852), private polygamy (1838-ish), John C Bennett’s exposé (1842), Danites (1838), and Nauvoo-era doctrines on Godhood (1840-44). The violence, lechery, secrecy, polytheism, and economic power undergirding the various hypotheses, though already associated with Mormonism to a certain extent, had not yet established themselves fully as part of the Mormon image and to nowhere near the proportions that they would later assume. 
Furthermore, folks had been handing out horns literal, metaphorical, and metaphysical since before (long before) Joseph Smith’s birth (cf. Jews).  For example (1808, London):
When our country threw off the yoke of Rome, the Spanish priests persuaded the people, that the English, in consequence of becoming heretics, were stripped of their former shape, and had horns like the devil, and satan’s cloven foot. It was therefore not without astonishment, that the first time an embassy was sent from England to Spain, the persons who composed it were seen to have undergone no change of form, in consequence of the change of their faith; but were as handsome and well shaped as if they had still continued within the pale of the Romish church. 
There it is: the familiar story, familiar before it applied to Mormons. Horns seemed to be something of a package deal in which the description was assumed for outsider groups and only later were specific attributes of the group correlated to the previously-alleged behavior. Mormons didn’t “grow” horns; the horns were already there, floating about brow-level in the cultural atmosphere. Mormons walked into them and they stuck.
Second, Mormons weren’t the only ones: horns were more popular than cholera. In documents generated between 1800 and 1945, I found alleged horns for Abolitionists , Americans , Blacks , Canadians , Catholics , Democrats , Englishmen , French Canadians , Frenchmen , General Sherman , Germans , Lord Byron , Masons , Protestants , Suffragists , Whites , Wisconsin politicians , and Yankees. I didn’t put a note for Yankees because everyone knows Yankees have horns. Duh.
Actually, it turns out that Yankee horns are kind of important and I’ll deal with them in a separate post. Suffice it to say for now that Mormons made up a small part of the horned herd.
Bonus Horns: Japanese WWII Anime
A World War II Japanese propaganda film shows the Allies with horns.
Mormon Horns 1, 2, 3, 4, 5, 6, 7. These horn posts continue earlier efforts analyzing ways of describing Mormons or using Mormons to describe something else. These include: India, Cows, Bluebeard, Lice, Crickets, Flies, Happy Valley, and sundry other beasts.
 These various factors might have reinforced or polygenetically inspired the horns imagery later, but they cannot account for the horns’ beginning. Since the total amount of time is relatively small, truly independent polygenesis seems unlikely.
 I didn’t look any earlier than the nineteenth century, figuring that the almost four decades before the first Mormon horns provided plenty of time to determine both whether the horn trope predated Mormonism and whether it had any currency simultaneous with Mormonism. (Besides, I already knew that Catholics and Protestants had been swapping horns for centuries and only agreed that Jews always had them.)
 David Bogue and James Bennett, The History of Dissenters: From the Revolution in 1688, to the Year 1808, 4 vols (London: Williams and Smith, 1808), 183.
Other examples: [A man dressed and (un)groomed as an indigent, asking for hospitality]: “I was standing at the glass behind the door, and the man did not see me until I awakened his attention, by seizing a handful of bread out of his basket to appease my hunger, which was rather an agony than an appetite; upon which he started back as if he had seen a hobgoblin. …[addressing someone who knows his true identity]: ‘I have asked for a basin of water, but cannot get it; the folks stare at me when I speak, as if I had horns and hoofs.’” John Mathers, The History of Mr. John Decastro and His Brother Bat, Commonly Called Old Crab, 3 vols (Boston: Wells and Lilly, 1815), 3.172-3.
“Seeing Professor Martyn, then proctor, approaching, he [the letter writer’s friend] rushed out of the coffee-room… to avoid being seated near so great a man. This we both regretted; and Martyn said, ‘… I am very sorry that he was so scared at my horns and hoofs.’ In allusion to which, when my friend, in process of time, became Proctor himself, he pleasantly wrote me word, ‘That he was almost afraid of looking into a glass, for fear he should see his own horns and hoofs.’” Baptist Noel Turner, “4. Johnsonian Letter the Third,” 1819 Nov 15, in Illustrations of the Literary History of the Eighteenth Century: Consisting of Authentic Memoirs and Original Letters of Eminent Persons; and Intended as a Sequel to The Literary Anecdotes, 8 vols, edited by John Bowyer Nichols (London: Nichols, Son, and Bentley, 1831 [1817-1858]), 6.165 [164-71].
 [Horace White, speaking of Owen Lovejoy]: “The fame of Lovejoy as an Abolitionist had preceded him, however, and the people gathered around him in a curious and hesitating way, as though he were a witch who might suddenly give them lock-jaw or bring murrain on their cattle, if he were much provoked. Lovejoy saw this and was greatly amused by it, and when he made a speech in the evening, Mr. Lincoln having made his in the day-time, he invited the timid ones to come up and feel of his horns and examine his cloven foot and his forked tail.” Horace White, quoted in William Henry Herndon and Jesse William Weik, Abraham Lincoln: the True Story of a Great Life, 2 vols (New York: D Appleton, 1895), 2.112.
 “London at last, and I ‘m stoppin at the Greenlion tavern. I like the lan’lord very much indeed. He had fallen into a few triflin errers in regard to America—he was under the impression, for instance, that we et hay over there, and had horns growin out of the back part of our heads—but his chops and beer is ekal to any I ever pertook.” No author listed, “Artemus Ward in London,” Punch, or The London Charivari (1866 Sep 01): 95; spelling as in original. Momotar?: Umi no Shinpei [??? ???? Momotaro’s Gods-Blessed Sea Warriors], an animated World War II Japanese propaganda film directed by Mitsuyo Seo (Japanese Naval Ministry, Shochiku Moving Picture Laboratory, 1945) shows allied (not just American) soldiers with horns. (In the linked YouTube, segment 9/9, time 7:20 shows a clear image of the horn. The horns are visible from about 9/9, 6:00 on; before that it’s cute animals singing, working, and training for war. [Disclaimer: I didn’t watch the whole thing; I just skipped through.]
 “It seems that the whites are as glad to find no horns or knots on the colored brethren as the colored brethren are to find all smoothness and evidence of Christian fellowship from the whites.” “Co-operation in the South,” The Home Mission Monthly 19:2 (1897 Feb): 62 [60-63].
 “There are thousands of fishermen and the wives of fishermen on the southern and north-eastern coasts who believe to-day that Canada is a land of demons and monsters, just as the more ignorant Southerners of the States during the Civil War believed the Yankees had horns and tails. The most singular legends exist in the bosom of these humble families.” Beckles Willson, The Tenth Island: Being Some Account Of Newfoundland, Its People, Its Politics, Its Problems, And Its Peculiarities (London: Grant Richards, 1897), 90.
 1843: “I knew if I had told you that Bishop England was there, you would have expected the roof to fly off, or thought the old fellow himself had come to frighten you; but no harm has happened; he had neither horns nor cloven foot, and will be very glad to see you at mass next Sunday, to return the compliment”; 1876: “It is true, Protestants here no longer believe Catholics have horns”; 1893: “Possessing, as they did, every natural virtue, this Lutheran family had been educated in the belief that Catholic priests were monsters, the emissaries of Satan; that they had horns on their forehead, like their master, and would bring disaster on a Christian household”; 1903: “My earliest impression were that the Jesuits had horns and hoofs and tails….”
No author listed, “Irishmen in America, and so on,” The New Mirror 1:8 (New York: 1843 May 27): 119 [116-9]; James O’Connor, “Anti-Catholic Prejudice,” American Catholic Quarterly Review 1:1 (1876 Jan): 12 [5-21]; Richard H Clarke, “Our Converts,” The American Catholic Quarterly Review 18:71 (1893 Jul): 559 [539-561]; Robert B Schwickerwath, Jesuit Education and Its History and Principles (St Louis: B Herder, 1903), 210.
 “I was brought up in the most republican corner of the most republican state in the Union, Massachusetts. I was a large girl before I knew that democrats did not have horns and hoofs.” Kate Upson Clark, “Who Is a Patriot?” in Official Report of the General Federation of Women’s Clubs’ Fifteenth Biennial Convention, June 16-23, 1920, Des Moines, Iowa, Mrs. Adam Weiss, ed, (no pub info), 81 [76-82].
 “When our country threw off the yoke of Rome, the Spanish priests persuaded the people, that the English, in consequence of becoming heretics, were stripped of their former shape, and had horns like the devil, and satan’s cloven foot. It was therefore not without astonishment, that the first time an embassy was sent from England to Spain, the persons who composed it were seen to have undergone no change of form, in consequence of the change of their faith ; but were as handsome and well shaped as if they had still continued within the pale of the Romish church.” David Bogue and James Bennett, The History of Dissenters: From the Revolution in 1688, to the Year 1808, 4 vols (London: Williams and Smith, 1808), 183.
 “The first foreign immigrants were the Irish…. While not openly maltreated… they did not receive a hearty welcome. …Something of a community of feeling was brought about, however, by the later arrival of a common enemy, the French Canadians, to whom, curiously enough, the Irish, in spite of the identity of their religion, were quite as hostile as the native Americans. …By a happy chance, the first Frenchman who ventured into Brompton is still living there; by a happier chance, he has a sense of humor. He loves to tell of the mingled curiosity and abhorrence his appearance excited. ‘They had no notion of what a Frenchman was like,’ he says. ‘They stared at me and whispered about me as if I were some strange animal. For a long time they couldn’t make up their minds whether I had horns under my hat or not, but in the end they decided that I had.’” Alvan F Sanborn, “A Massachusetts Shoe Town,” The Atlantic Monthly 80:478 (1897 Aug): 178 [177-185].
 On the march of some French prisoners from Portsmouth to London, the country population, inflamed with hatred and fanaticism, were convinced that Frenchmen had black skins, horns on the head, and cloven feet, and were astonished to find that they were like other men. A village schoolmaster brought his scholars to see them pass: they opened their eyes wide and cried out with a disappointed tone:—‘But they have not got any horns! Mr. Thompson and you told us that they had: where are the horns, Mr. Thompson? ‘Silence, you little monkeys,’ said Mr. Thompson, evidently as much disappointed as they were.” Footnoted to Souvenir d’ un prisonnier Français, in Charles Heneage Elsley, An Essay on the Relation Between the English and French Languages (London: Whittaker & Co, 1858), 87.
 “We were the first German prisoners to come to America and people were very curious about us. When we arrived at the station in Illinois, hundreds of people were there to see the ‘Nazis’, as they called us. …They had some fantastic ideas about us. Later we were told that the Americans had been told that the Nazis had horns and hooves. They believed it. So, when we were led out from the train, we heard children asking, ‘Where are the Nazis’ horns and hooves?’” Herbert Beyer, quoted in Bob Carruthers and Simon Trew, Servants of Evil: New First-hand Accounts of the Second World War from Survivors of Hitler’s Armed Forces, ed by Simon Trew (St Paul: Zenith, 2005), 249.
 “A correspondent of the Madras Mail, under the signature of “Œdipus,” attributes the separation between Lord and Lady Byron to the fact, that Byron was really a ‘devil incarnate’ with rudimentary horns and tail and cloven feet, after the true Satanic type. This would be ludicrous if it were not sad.” No author listed, “The Byron Mystery,” Notes and Queries 4, 4th series (1869 Dec 11): 527.
 “As General Sherman was riding through the streets of the Gate City, he was pointed out to a company of blacks, gathered on the corner. “ ‘Lord, massa, is dat General Sherman ?’ said one of the old men. ‘Why, bless your soul, dey tell us he had long whiskers, way down to his knees. Dey told us he had big eyes and ears, and had horns. Why, Lord bless my heart, dat General Sherman ? Why, all of us niggers used to run when dey holler Sherman. Why, all de white folks run. Lord, it made old Johnson run to hear of dat man. I’se glad I’se seen him, though I just wanted to see de man what made my old massa run.’”George Whitfield Pepper, Personal Recollections of Sherman’s Campaigns in Georgia and the Carolinas (Zanesville, OH: Hugh Dunne, 1866), 171.
 “The good people of Oberlin saw that Masons did not wear horns and hoofs, and were astonished that many clergymen were members of the Order.” Thomas F Gibbs and William R Singleton, “District of Columbia, Washington, 18th Correspondence, 1890 Dec 12,” in “Report on Foreign Correspondence,” Proceedings of the Grand Lodge of Free and Accepted Masons of the State of New York, One Hundred and Tenth Annual Communication, June, 1891 (New York: J Little, 1891), 13 [13-14].
 1855: “[T]hough sent as a recruit into the fire, he [a Protestant missionary] has shown himself to be a good soldier, and that in a country where, as he tells me, there are still people who seriously believe that Protestants have horns”; 1893: “A few years ago, I happened to meet a Protestant lady, who told me the following story: When she was quite young she visited a Roman Catholic family….. She was received very kindly; but some days afterwards…nobody would speak to her. …At last, the landlord went up to her begging permission to touch her forehead. After having done so, he exclaimed, ‘Are you really a Protestant? You have no horns! We have .been told by our priests that all Protestants have horns as being associated with Satan!’ You can find, to-day, the same opinion spread among the Roman Catholic inhabitants of southern Austria”; 1898: “The priests, in order to frighten their ignorant parishioners from hearing the Gospel, had graphically portrayed the American missionaries as incarnations of the evil one himself. Ines, in common with his neighbors, had been told that as soon as the Protestant preachers opened their mouths to utter their heresies, sulphurous flames issued out of their mouths, horns appeared on their foreheads, and cloven hoofs took the place of feet”; 1910: “While the medical missionary lived in Ciudad del Maiz, Doña Pancha came one day for medicine. She had never dared to enter a Protestant’s home, for she had been told that they were devils with great horns. But now, for the sake of the medicine, she braved the danger.”
NB Millard, letter 1855 Jul 03, “Germany,” Monthly Extracts from the Correspondence of the British and Foreign Bible Society 6:52 (1855 Aug 31): 578 [577-9]; Rev Dr Pindor, “Austria: Evangelical Church in Silesia,” Evangelical Christendom 47 (London: 1893 May 01): 145 [145-8]; William Wallace, “Gospel Triumphs in Mexico,” The Missionary Review of the World 21:8 old series, 11:8 new series (1898 Mar): 193 [190-193]; James G Dale, Mexico and Our Mission (Lebanon, PA: Sowers Printing, 1910), 175.
 “Ridicule was the chief weapon of the press. We were caricatured in all the papers until really the majority of people supposed that the women on the suffrage platform had horns and hoofs. And now, as we sit here, how changed is the scene!” Elizabeth Cady Stanton, Report of the International Council of Women, Assembled by the National Woman Suffrage Association, Washington, D. C., U. S. of America, March 25 to April 1, 1888 (Washington DC: National Woman Suffrage Association, 1888), 325.
 [Describing Baptist missionary life in Burma]: “The prospect for the mission is most encouraging. …We are living in a most primitive way. There is not much luxury about it I assure you. …One old man sidled up to me as I was writing a little while ago, and asked me confidentially if ‘it was true, as he had heard, that some white people had two heads, and that others had horns. Is there not some ignorance to combat here?” Alonzo Bunker, “On the Frontier of Upper Burma,” The Baptist Missionary Magazine 80:5 (1900 May): 180 [178-181]; “It seems that the whites are as glad to find no horns or knots on the colored brethren as the colored brethren are to find all smoothness and evidence of Christian fellowship from the whites.” “Co-operation in the South,” The Home Mission Monthly 19:2 (1897 Feb): 62 [60-63].
 “The governor departed somewhat from his usual practice by here calling attention to the fact that he didn’t have horns and referring to the tactics of the local stalwart leaders and to the newspaper abuse to which he was being subjected.” Albert O Barton, LaFollette’s Winning of Wisconsin, (1898-1904) (Madison: Homestead Co, 1923), 429-30.
 Momotaro: Umi no Shinpei [Momotaro’s Gods-Blessed Sea Warriors], directed by Mitsuyo Seo (Japanese Naval Ministry, Shochiku Moving Picture Laboratory, 1945). In the linked YouTube, segment 9/9, time 7:20 shows a clear image of the horn. The horns are visible from about 9/9, 6:00 on; before that it’s cute animals singing, working, and training for war. [Disclaimer: I didn’t watch the whole thing; I just skipped through.] Video 1/9; Video 9/9, 7:22.