We took I-40 East from California to New Mexico then I-25 North to Colorado then South Dakota in late December a couple of years ago. It was a great trip!! All the Highways were clear and ice-free. In Colorado, we drove on a couple of smaller roads that weren't plowed and I was really surprised how well the RV did; it must be all that weight. I just took it very, very, very slow in that stretch.
3 stops that we made that I would definitely recommend are: South Rim of the Grand Canyon, the Grand Canyon Taverns, & Meteor Crater.
The only problem we encountered was all the pipes & the toilet froze overnight in New Mexico. Also, the heater seemed to not work as well as it usually does, not sure if that was the elevation or the cold, but I've never had the problem since. Maybe I'd suggest bringing an electric heater and running the generator if necessary.
Also, we managed to avoid campgrounds. We spent one night in a casino parking lot, a bunch of nights at rest areas, a night at a wal-mart. We originally planned to spend a night in a campground at Grand Canyon, but we cancelled it in favor of continuing back down to a lower elevation in case the weather got bad. You've got to remain flexible in either direction to avoid the really bad weather. We even spent 1 night on our return trip in a flying J. It was loud with all the trucks, but when you're that tired, that sign is a welcomed sight.
We run I40 from OK city to calif about twice a year. OK city is a rough patch but the rest is pretty good ganerally. I get the 7 day forcast for the stops along the way and usually get it right. From Branson Mo we stop in Amarillo, Gallup, Williams and visit friends in Kingman for a couple of days before hitting the Peoples republik of Kalifornia. If the weather is good in Amarillo we hit there first, if not we head south to a point just N of Dallas then head down I20 to I10. If the weather is good to Albequerque (sp) but not beyond, we go south there to I10. It's loosey goosey, drives the wifey nuts.
You get altitude even going I10 and Ice storms are possible. Just gotta keep an eye on the weather and move when you can. The trip west is harder to plan because the weather patterns start there and work east. Coming the other way you can plan to get between storms and ride good weather all the way if you keep moving.
I have a couple of hard rules, i won't drive in fog or ice storms.