First let me suggest that you might find it cheaper and more comfortable during ski season to rent a cabin or condo (along with a car for transportation), than to buy an RV and try to find a campground open that time of year in the Colorado ski country.
However if you go the RV route, you might note that if you drive that RV (or anything) in the mountains in winter, it's likely there are times the "chain law" will be in effect, meaning that chains will be required. Of course if you can wait a few days (or sometimes just a day), you may be able to find a time when you can travel. Still, there are often a lot of bright sunny, even somewhat warm days up there during the winter, so you might get lucky. You'll probably also want to check on the proximity of grocery stores to your RV site.
When you look at a listing of things "in the area," note that sometimes "near" or "close" may mean within 20-50 miles, depending on the specific context.
Some ski areas to Google for might be Aspen, Vail, Steamboat Springs, Winter Park, Breckenridge, Summit County, Purgatory, and likely others I can't think of right now. Of course a lot depends on what else you might want to see on your trip, but so much is closed or difficult to access in the winter.
Still, some RVers who ski may have some good ideas for you.
As for Utah, if you're looking at such places as Bryce, Canyonlands, Arches, etc., weather permitting you can enjoy them a lot. Good luck.