I didn't see Jack's green coat in the closet. I don't think it was there.

About the difference between "cowboys" and "ranchers": Here's a tidbit on what Annie Proulx has said in an interview:
Interviewer: I think it's clear to anyone who reads "Brokeback Mountain" that above all it's a wrenching, starcrossed love story. It is about
two cowboys, but it seems inaccurate to call it gay literature.
Annie Proulx: Excuse me, but it is
NOT a story about
"two cowboys." It is a story about two inarticulate, confused Wyoming ranch kids in 1963 who have left home and who find themselves in a personal sexual situation they did not expect, understand nor can manage. The only work they find is herding sheep for a summer
some cowboys! Yet both are beguiled by the cowboy myth, as are most people who live in the state, and Ennis tries to be one but never gets beyond
ranch hand work; Jack settles on rodeo as an expression of the Western ideal. It more or less works for him until he becomes a tractor salesman.
sam