Male missionary in the Southwestern States Mission in the early 1900s proselyted ?without purse or scrip? (WOPOS).  If they could not persuade someone to board them for the night, they ?slept with Uncle Sam? ; if they could not persuade someone to give them food, they went hungry. WOPOS was taught as both doctrine and policy.
Mission President Duffin emphasized the policy: ?At all of the conferences which I have attended, I have impressed upon the Elders the importance of traveling without purse or scrip?.?  Duffin and many missionaries understood WOPOS as a doctrine:
A very pleasing feature of the reporting of the Elders was their testimonies with regard to the principle of traveling without purse of scrip. They felt that this was the proper way to preach the gospel, and testified that since they had been doing this God was greatly blessing them. [iv]
WOPOS also appeared in sermons in company with duties and virtues. 
So? what did the travelling Elders in this study think of WOPOS? I don?t know.  Their diaries are book-length disquisitions on the difficulties of the ?lifestyle?—and testaments of the Elders? fidelity to it—but the diaries do not contain any explicit critiques of WOPOS that I have noticed.
I do notice, however, a few ?workarounds?: missionaries sometimes supplemented their diets with store-bought snacks; rotated sleeping among the homes of friends; and sold books or clothes when they needed money for food or lodging.  Elders also sometimes ?talked hard? to persuade someone to keep them for the night. 
Elders Brooks and Folkman report renting rooms while working in the cities of Orange and Galveston, respectively. Elder Folkman came closest of the diarists to verbalizing the ineffectiveness of WOPOS in cities.
July 2, 1900. Monday. Went to the P. O. Received a letter from Pres. Duffin telling us to discontinue renting a room and go and depend upon the Lord to open up the way for us, which came like a blow to us all. We got the consent of the conference pres. to rent the room and then word comes from headquarters to get out. Of course we have to obey, but we will stay untill after the 4th of July. 
Neither of the female missionaries in this study proselyted WOPOS (and I assume this was true in general). Once, when Sister Carling and companion were out later than usual, they reflected on the Elders? situation:
While passing along this road at this time of night brought to us some of the experiences which the Elders have in their travels. We thought how we would feel if we were strangers in that part and were seeking entertainment and knew not who would take us in. We felt thankful to Father in heaven for the many blessings and kind friends he had blessed us with. 
The ?Southwestern States Mission? series (homepage) examines mission life in (mostly) Texas around 1900.
 For a broader overview, see Jessie L Embry, ?Without Purse or Scrip,? Dialogue, 1985, vol 29(3): 77-93. I acknowledge the infelicity of ?WOPOS? but protest that using a series of euphemisms like ?itnerant penury? or writing out ?without purse or scrip? a dozen times in a four-hundred word post is worse. I will use WOPOS both as a direct replacement for ?without purse or script? and as an unofficial title for the style of missionary work: ?The missionaries proselyted WOPOS.? ?WOPOS was taught to missionaries as both doctrine and policy.?
 I find ten instances of some variation of ?sleep with Uncle Sam? and one instance where ?Uncle Sam? seems to refer to the federal government. ?Night came on us about midway, it seemed it was almost impossible for me to go any farther. There was no one living on the road and I hated the idea of sleeping with Uncle sam, so we kept plodding away.? (Brooks, 1901 Mar 13 Wed); ?it being So late the People was all in Bed So we go back to the School house and make a good fire and Stretch our Selves out on the Benches But O how hard they were before morning after being used to Sleeping on feather Beds the 4th night in uncle sam’s Beds Since I came to Texas? (Clark, 1901 Mar 29 Fri); ?So after Supper we leave Town go about two miles and Stop By the Road Side have our Prayers then we felt constraint to not go and get lodgings to a house as there might be a mob raised against us and they would easily find us So we remained in the timber all night by the Road Side So once more we take lodgings with uncle sam. we Lay down on the Sand and was Soon a Sleep dreaming of Home Sweet home? (Clark, 1901 Aug 28 Wed); ?There was few come out to meeting and we did not hold any and as no one asked us to go home with them, we had to use Uncle sam for a lodging place. We went in an old shed but we got so cold we had to move out in the woods and make a fire and spent the night this way.? (Folkman, 1900 Mar 24 Sat); ?On awakening early in the morning we found that Uncle sam did not have breakfast ready. But shouldering our grips we started on, traveling about 8 miles without anything to eat.? (Jones, 1899 Nov 18 Sat); ?we leave our lodgings and go and take Breakfast with uncle sam and feast on Texas air it doesn’t fatten anyone.? (Clark, 1901 Sep 05 Thu); ?The Elders was not there. So we wait until afternoon when they Showed up. then we all go just out Side of town and all remain together in the Timber all night So we could remain together. we would rather Stay out and Set By a fire then Separate from each other. we are So pleased to tell our Experience to each other. So we Set up with Uncle sam.? (Clark, 1901 Oct 21 Mon); See also Clark, 1901 Oct 23 Wed, 1900 Jun 10 Sun, and 1901 Nov 01 Fri. US = federal government: ?Bro. Street, a young man from Utah, a Mormon, who was working there in the interest of Uncle sam, asked me to go to the hotel with him.? (Jones, 1902 Feb 15 Sat).
 Duffin, 1900 Sep 24 Mon; ?I impressed upon them among other things the necessity of doing their work strictly without ?purse or scrip?? (Duffin, 1900 Aug 24 Fri). Also such teaching is mentioned or implied: Duffin, 1901 Mar 4 Mon; Duffin, 1902 Aug 24 Sun; Duffin, 1904 Mar 20 Sun. In a 1902 visit, Apostle AO Woodruff reiterated that Elders were to ?travel without purse or scrip? and further counseled: ?do not wear out welcome by staying too long with people.? (Duffin, 1902 Nov 17 Mon).
 Duffin, 1901 Mar 4 Mon. One of the Elders (not in this study) reported being ?converted to traveling without purse or scrip?; another said he had ?traveled without ?purse or scrip? and the Lord has blessed us.? (Duffin, 1904 Mar 20 Sun). More such examples are in the Southern Star, the mission newspaper for Southern States Mission. Contrast the religious language here about WOPOS with the matter-of-fact language (and general lack of comment) about sharing beds.
 ?the importance of traveling without purse or scrip, studying the standard works of the church, the Bible, Book of Mormon, and Doctrine and Covenants, obedience to the counsels of the priesthood? (Duffin, 1900 Sep 24 Mon); ?missionary work, obedience to counsel of priesthood, character building, traveling without purse on scrip, methods of study, courage in missionary work? (Duffin, 1902 Aug 24 Sun). Note that the 1902 Aug meeting was in Chicago while Duffin was visiting outside the mission.
 President Duffin started out as a travelling Elder and even then treated WOPOS as a spiritual ideal: ?Went into the city today and got our shoes mended, without costing us anything. We have always been blessed in getting anything we needed so as we obey the counsels of the Lord and ?travel without purse or scrip.?? (Duffin, 1900 Jan 25 Thu). Sister Cluff (not a travelling Elder) also used the ?someone gave us X for free; the Lord blesses us? formula.
 I haven?t gone through and tracked sleeping locations exactly. Elder Brooks in particular spends much time sleeping at the same four or five houses.
 I do not know if the Elders would describe ?talking hard? as a consequence of inadequate faith (?if we had more faith the Lord would have blessed us with a place to stay?) or as an expression of faith (?I have faith the Lord will magnify my efforts to find a place to sleep?). Examples: ?At night, tryed two places at Cat Springs and could not get a place to stop. At last after we talked hard, we got in but had to go to bed without supper.? (Folkman, 1900 Oct 26 Fri); ?At 7 p.m. we came to Bro. Walker?s. After talking hard to him, we were granted the privilege of staying. He said that there were so many tramps traveling over the country that a person did not know whether they were clean or not. I assured him who we were.? (Jones, 1901 Oct 21 Mon); ?After dinner we went on 8 miles further and as night was drawing on, we began to seek for a place to stay and were refused three times, but after talking awful hard we got into Bro. Whetherby?s place.? (Jones, 1899 Nov 18 Sat); ?When we got in about two mile of the town of Burton, we left the R.R. and began asking for shelter. Stopped with a German as usual. He didn?t want to take us in at first, but we talked him into the notion.? (Brooks, 1900 Apr 25 Wed); ?We then started on west. We traveled about three mile, began inquiring for shelter. Were refused six times. There were no American people living there?all Germans. One man told us to go to the next place. If we couldn?t stop there, we could come back and stop with him. Went to the place. The man wasn?t there so we went back. When we got there, the lady came out and said they couldn?t keep us. It was then dark. She let her little boy go with us and show us the way to another house. When we got there the man said he didn?t have room. We talked pretty hard to get him to keep us, but he wouldn?t do it. He went and showed us the way to another place. We succeeded in stopping at that place and I was very thankful for it.? (1900 Apr 05 Thu).
 Folkman, 1900 Jul 02 Mon.
 Carling, 1901 Dec 03 Tue, p 77-78. One of the issues early Sister missionaries dealt with seems to have been the propriety of women carrying things in public. Sister Carling records two instances: ?We were to go to Bro. Hasty?s that evening so Elder Judd carried our bundle which we usually took down there with us, which the men folks laughed at. It was our clothes to laundry. We did our laundry work down to sister Hastys. The road was muddy so we found out a little about Kansas mud, before we got to the place.? (Carling, 1901 Dec 06 Fri p 81-83). ?On our way home from Jay we were worrying about how we would get all our baggage up to the office from the car but it happened that two of the Elders were at the corner when we got off the car so they relieved us of all our parcels and we walked up the street to the office, quite respectable looking girls.? (Carling, 1901 Dec 10 Tue p 84-86).