Woodalls directory should tell you which RV parks (if any) are open year round. There are a couple North of Missoula on Hwy 93 that might be.
Having done a couple of winters in Billings, one in a Suncrest Class A and one in a 32 foot fifth wheel, I recommend skirting around the coach. I used 48 inch wide Reflectix wrapped around the coach and covering the grille and windshield. I built the water line with hard copper tubing, installed heat tape according to the instructions, and wrapped it with fiberglass pipe insulation. I left the grey water dump valve open all the time, and opened the black water only when necessary. The sewer hose did not freeze. I had V-1 Propane bring an 80 gallon tank out to connect to the fifth wheel, and they kept it full. On the Suncrest, I used a 100 POUND bottle, and that was a nuisance when it got cold. The larger tank, filled as needed by the distributor, was MUCH better! In the Suncrest, there was considerable cold air leakage around the door, so we bought a blanket from a thrift store and hung it as a draft blocker. It helped greatly. I installed window film on the inside of the windows, and that also helped. We bought the foam plugs for the ceiling vents to insulate them.
I can't say that we were totally comfortable, but we survived nicely. Looking back, I almost wish we had rented an apartment!