That's the same route Ramius and I drove across once before Christmas. We got lucky and had no snow anywhere. I don't remember the Rockies being hairy, in fact, there's a wide gap there in the mountains in WY where we could see the mountains on each side of us in the distance but we weren't in them. We drove from Denver to Pocatello ID in one day, and Pocatello home the next.
Last year there was a lot of snow here in April when I got here - some of the local folks I talked to said that was typical. It's very dry this time of year, so it may not be such a bad time to travel, I dunno.