Not in my real life or even my unreal life. I read it long ago in an account purported to be spoken by a cowboy. So it was in a book but not in a western, unless of course I’m just misremembering.
However, your point is well taken. The realities of cowboy life probably included a lot of manual labor. But that didn’t preclude the cowboys themselves from having some construct of an idealized life, or their own fictionalized version of reality. “Carpenters” do everything from digging ditches to fine woodworking. It’s very likely, though, that the guy installing custom moldings would consider certain jobs beneath him, not because he’s never done it, but because he never wants to have to do it again. In my experience it’s also true that every person has an idea that a certain level of work is beneath him or her. The “I don’t do floors” syndrome. My suspicion is that there was a job description of “cowboy” which gave the occupier of the job the sense that he was a little better than the ordinary worker. It was specialized, skilled work.
Of course, a few people I know have no pride and will do absolutely anything required, but they run their own businesses and have plenty of money.