Josh writes (succinctly): Cowboy boots?
The short answer is: if you have to ask, no.
If you’re a cowboy, or live in a cowboy place, then yes, western boots, and indeed western clothes generally, are fine. There are places in this great country where men wear cowboy boots with suits, and while it isn’t exactly the height of taste, I wouldn’t deign to correct them. It’s a cultural thing. If you’re that kind of guy in that kind of place, then go for it. Western clothes are one of America’s great contributions to the world of style.
That said: if you’re not that kind of guy, then no way. I have always wished I could wear western shirts, but I have never looked like anything other than a total tool in them. This is because I am much more George W. Bush than I am Sam Houston. If there is doubt, err on the side of caution.