Rick has a good point, one that immediately came to mind as I was reading your post: winter and conversion vans aren't good companions when it comes to sleeping arrangements. The only way I'd consider sleeping in one during the winter is with a good 4-season sleeping bag!
If Grand Canyon doesn't appear to work out because of snow/ice, you could consider Saguaro National Park and the Arizona-Sonora Desert Museum, both right outside of Tucson. Saguaro NP is in two sections, one on the southwest side of town and one on the east. One is a thick forest of the tall cacti, and the others are very, very old cacti. There's Kerschner Caverns nearby, as well as an old movie set, Old Tucson. Then further along the 10, you could detour up to Carlsbad Caverns National Park, or south to Big Bend National Park.
Donna