Arizona will be warmer in Feb/March than New Mexico and Santa Fe will definitely be colder. If you make it up there perhaps on your return home, Santa Fe Skies RV will have a site for you. If you only have 3 weeks from southern California then don't plan on going too far into Texas. There's a lot of nothing from west to east until there's 'something'.
One place in Texas you could go is Big Bend National Park and perhaps check out the Fredericksburg, TX area on your return.
The Tucson/Benson, AZ areas at that time of year will be nice. Kartchner Caverns State Park in Benson has a nice campground with hookups and the cave tour is great. If you want lots to do in Tucson, try to stay at the Voyager RV. You'll then be close to the area attractions - the Desert Museum is a must. It's not a typical indoor museum. It's outdoors with animals, butterflies, hummingbirds, flowers.
Have a great time!