For Winter... I'd suggest Arizona. Southern Arizona has great winter weather and lots to see and do.
We love New Mexico - but Northern NM is where much of the great sightseeing is, and it's gripped by winter due to it's higher altitude. May/June is an excellent time to visit NM.
Texas is great - but Winter weather is so variable. First it's so big that north texas has a fairly real winter while deep south texas can't be pinned down to the season you'll encounter. We're just north of San Antonio. It's 80's today but it was 30 5-days ago and will be in the 50's the day after tomorrow. Honestly. Mar/April is better for TX. Many snowbirds spend the Winter in the RGV (Rio Grande Valley) because the weather is predictably warm that far south. It's just not the most interesting place in Texas to visit.
We spend Jan/Fed in Tucson and it's usually sunny, warm days with cool nights and very little humidity.
Be aware that between Palm Springs, California and Arizona that hordes of RVs show up in the Winter. If you're planning on moving around you should find it easy to find places to set up camp. If you want 2-months in one place you should make reservations right now - or better yet 4-months ago. Don't forget that Northern AZ has a cold snowy winter again due to altitude.
2017 Winnebago Adventurer 37F
2016 Lincoln MKX Toad