Woo hoo! I love answering questions about my relatively obscure academic field (and this one is great! = )

So, let's define our terms, shall we? "Wild West" can mean a lot of things to a lot of people, but for the sake of brevity, I assume you mean the American western frontier (so all land in the current continental U.S. west of the Mississippi River), roughly from the time after the American Civil War to the end of the 19th century (so 1865 - 1899). Even with that point of clarification, you have to understand that this time and region encompasses A LOT of variance. Like, let's take climate differences, for example. What a person would wear in Denver, CO vs. Tucson, AZ would have been pretty different, and depending on that person's professional or social distinction, there could be even more variance.

So, just to give a few examples, let's talk about actual "cowboys," as in men who worked with cattle, rode horses much of the day, and fit the classic archetype. During this period (1865 - 1899) they were commonly referred to as "punchers," and were about as salty, tough, and hard-nosed as you might expect from popular culture stereotypes. (These were not outlaws, i.e., the Billy the Kid or Jesse James types, though...more on that in a minute). So a legitimate cowboy (puncher) would have had just one set of clothes that they wore for a drive, which could go on for 2-4 months. They might have changed a shirt from time to time, but for the most part, these guys had one set of clothes when working, and when the drive was over, they tossed it and got a new set (except, maybe, for their hat and duster). So, speaking of dusters, this is your long, trenchcoat-style jacket that dropped down to about mid-calf, and was usually worn open (buttoning it in the saddle created problems as it was likely to catch on the saddle horn). When in-camp, and off a horse, it might be buttoned to protect one's self from the cold, but usually a buttoned vest took care of this. This is the next most vital piece of clothing, as the vest actually would have been nicely lined, and did a great job keeping body heat in. Below this would have been a button-up long sleeve shirt (likely cotton or wool). Denim didn't really go mainstream until the 20th century outside of California, so "trousers" would have been the norm for pants. A large handkerchief/bandana would have been pretty common as well, as dust was a major concern for a real puncher, and having one would have been almost as indispensable as a hat. Lastly, the hat. Cowboys absolutely wore them, and would have rarely been without theirs. These were not disposable, and cost a fair bit of money, and were, again, absolutely essential. Same thing with gloves to a lesser extent.

Outlaws were a different story. Depending on who they were, their background, and who they worked for (if anyone), this would have varied. Billy the Kid, for example, wore a lot of Mexican-styled clothing, and drew a lot of his influence from there. A guy like Tom Horn, on the other hand, preferred to look respectable, and often wore a suit similar to what you might see today (Wyatt Earp was similar when in Dodge and Tombstone). That isn't to say that Earp or his contemporaries always wore a suit: they didn't. And it is hard to say with any certainty EXACTLY what specific people were wearing on a regular basis, because it just doesn't come up a lot in the primary sources we have. Photographs were often staged (rarely spontaneous), and depending on a situation, a person might wear suspenders and britches one day (without a coat or vest...like, if they were just working in their fields), and a fine suit another.

It really does depend. For more reading, I might check out Richard Slotkin's 'Gunfighter' trilogy, or Michael Denning's 'Mechanic Accents.'