The most direct route will be trhough Idaho and Utah and also where the weather will be cold but snow should not be a problem if you travel on Hwy 84 to Hwy 93 and then south through Las Vegas. Not the most scenic route but the shortest. With this route you travel 1400 miles with a drive time of 21 hours. Possible stops include Boise ID, Wells NV, and Las Vegas.
An alternate route is I-15 via Salt Lake City but I greatly dislike driving through this area and its mandatory weigh stations for RV's and avoid it if at all possible.
