I wish you all a thoughtful and thankful Veterans Day. After a three-month break, I’m restarting the “Southwestern States Mission series” (homepage). A few months ago clothes dyeing came up in the Jones diary at Keepapitchinin:
We then started to Bro. Klaus’, a German, to wash and dye our clothes. …The kind sister prepared a nice dinner. After talking for a while I made known our wants and the answer was “you are perfectly welcome.” It took us nearly all afternoon. The sister helped us some. At night my coat and vest shone up with a fine black color. 
In the six (four almost-full-length) traveling-Elder diaries, I count 9 instances of dyeing clothes: Jones (1), Folkman (3), and Brooks (5). Dyed articles mentioned are: hat, coat, pants, vest, and generic “clothes.”
Like the Jones entry, almost all of the descriptions mention taking a long time and getting help from a woman. Elder Folkman gave the most detailed description:
[Thursday] “Elder Shipp went to Waverly and I went to Willis with Bro. Findley to get some Dimond Dye to dye my cloths.”; [Friday] “Started to prepare my cloths for dying. Washed them throu several waters then put them in the dye.”; [Saturday] “As the dye was dry in my clothes, we went to work to do the necessary wrensing. Put them thro. 6 waters. In the eveing they were ready for pressing. Sister Findley done that.” 
Elder Brooks notes a follow-up visit for running dye a week after the original dyeing. 
On slim evidence, I conjecture that coats got dyed after heavier use in the winter and pants got dyed in the summer after the wading caused by the spring and early summer rains. 
 Jones, 1901 Mar 27 Wed.
 Folkman, 1901 Mar 21 Thu, 22 Fri, 23 Sat.
 “During the day I wrenched my coat out as all the dye wasn’t out so was fading on my shirt. Sister Shirley pressed it for me. She also sewed my shirt up and washed it” (Brooks, 1900 May 17 Thu).
 With the usual caveats about sample size, the 9 instances occur mostly in Spring and Summer: March (3), May (2), June (1), July (2), October (1). Brooks and Folkman dye the most and are the furthest south, where it rains more and the ground is marshy/swampy; there might be a correlation. Coats are specified 5 times, in March, May, first half of June, and October; pants are specified 3 times, 2 at the end of July and 1 in October. The ninth instance, in March, is the generic “clothes.”