Contrary to what many folks believe, living in Billings is not akin to living in a freezer. In fact, I often tell people that Billings is the "Banana Belt" of Montana. One winter we were in the Palm Springs area--an area one expects to find balmy temps and sunny days. We found out that yes, it does rain in Southern California, and yes, it does get cold. In fact, the temperatures in Billings equalled or exceeded the temps in Palm Springs that year.
If you are a winter sports fan, there are many areas close to Billings that one can strap on their downhill/cross country skis or suit up for a day on a snowmobile.
Don't let myths of weather deter you. Billings is great year-round place to live. Now, West Yellowstone is a different story . . . .