Hi, hopefully some of the fashion experts will drop by to answer, but meanwhile, you might be interested in checking out some previous responses

• Did early modern and early, modern, women's clothing in the West reflect different climates? - not quite in the "Old West" but /u/colevintage gives a general introduction to the importance of fabrics in a hot climate

• People sure dressed in heavy clothes in the wild west (E.g. Tombstone, AZ). Are there any notable instances of negative consequences of this and/or how they managed to get along without proper air conditioning? - various comments on the importance of durability, fabrics, coverage. This thread, Maybe it is Hollywood, but did people in the south or "westerns" really wear the heavy clothes they portray them as? adds another upvote for wool

For reference, you may be interested in these

• Wild west clothing - /u/petite-acorn describes typical clothing

• Do people historically always dress nice in Western movies or movies always just want to depict that wearing vests/tuxedos is not a bad thing in a hot western atmosphere? - provides links to a few photo archives