Denver to Utah in January ??

There is a State Park in Rifle that is open all winter, and I think several State Parks in Grand Junction(Island Acres and Fruita) may be open for camping all winter. Check on their web sites.
As far as weather goes, I was in a snow storm in May going over Eisenhower and Vail. In Sept it was bright and sunny over the passes, and sleet/snow in Denver. Expect any/all weather between Denver and Grand Junction.