My daughter's a freshman there right now. She was originally brought up in NJ and even though she's a Montana resident now, she gets called "Jersey" occasionally. For the most part, the cowboy issue has been minimal. She likes rap and her roommate, a farmgirl from a tiny farm town, likes country, but they get along wonderfully. Other kids have come from NC, Puerto Rico, and Alaska. Naturally there are a fair amount of Montanans, but she says the feel is not "cowboy". I think you may run into differences in the demographics depending on your major and what residence hall you are in. She is in one of the "wellness" dorms and is a Biology major. I would imagine that if you are an Agriculture major you will have more farm and ranch classmates.
Most of the kids ski at Bridger -- it's closer and cheaper. Conditions there ski wise this year have apparently not been anywhere near as good as up here at Big Mountain (she comes home about every three to four weeks), probably due to the sunny weather mentioned above. (Since we have tons of fog at TBM, the snow lasts lots longer.) I think that the snow may be better over the course of the season at Big Sky since I think the elevation is higher than Bridger. Big Sky is definitely glitzy compared to any other MT area I've been to...I keep having to tell myself that it is not Deer Valley. The place is HUGE.
I do know that she is frequently telling me she is walking around in a tee shirt on campus when I have my "Nanook jacket" on up here.
Bozeman looks to be a cool town in terms of the stores, but one day I walked in and out of a few and the prices in some were pretty incredible (high) compared to Whitefish. Stuff I thought was overpriced at the place I work at was even higher there...lots higher. But, I think that students won't necessarily be shopping at any place but Walmart, so that issue may not affect you.