Maybe look at Cody? Close to great backcountry skiing, if sleeping giant opens you have a resort. Ice climbing is out of this world, and you can likely find south facing rock to climb all winter...
IJMayer wrote: lots of climbing near butte but not a large community. lots of small ski areas near by so you're bound to get your fill skiing. if you're looking for a remote rocky mountain town, what about lander? lots more climbing, but i don't know about skiing
Skiing in lander is a huge drawback. They do have nordic in South Pass, I think they groom the golf course or something in town...otherwise, it is off to Pinedale or Jackson for resort. Pinedale is a better option. Climbing community isn't huge but it is there... The wind river range is magical for climbing.