Welcome aboard the RoadTrip America forum.

The areas you want to get to rely on tourism, particularly skiing, for a large chunk of their economy. As Brad points out, the main thing you have to be prepared to do is be prepared for what may come. But the ski areas in Colorado and the National Parks in Utah will typically have their roads opened back up within a day of most snow storms. Pay attention to the weather - here in the US we have a television channel (available in most motels) that is devoted exclusively to weather - keep an eye on it. With a month, a flexible schedule, and some experience with winter driving, I see no reason to not do this trip. Just be careful when need be.

AZBuck