Chicago to LA in the winter in class C without a basement

Even the desert can see hard freezes now and then but I've never had plumbing in our RV freeze. There are a few areas along I-10 that can get dustings of snow but almost always only at night with it gone by sunrise.

Do not drive I-10 all the way through Phoenix unless you have reason to visit Phoenix. Instead take I-8 west to Gila Bend, then north on highway 85 to I-10 west. This bypasses the Phoenix traffic and congestion that can make a trip through Phoenix miserable!