First, I would recommend you rule out New Mexico for warmth in winter - even the far southern part. We tried it.
Since you're from Nashville why not test some areas for a few years? Begin with the closest Florida, southern Alabama (Gulf Shores), lower Texas from Rockport on down, southern Arizona or southern California. Each area is completely different. All the areas can have cold days/nights - scour the weather histories. Each winter will be different, sometimes rainy, sometimes cold, sometimes perfect (like Arizona was this past winter). You just have to accept that you'll have some bad with the good.
Regarding your narcotic prescriptions: that will now be an issue that you'll have to research with the new ruling in March.
Normal prescriptions are very easy to renew as you travel. Not so with narcotics. I'm not familiar with all the details but I understand you cannot get refills done. You need a brand new prescription by your doctor. Begin by talking with your physician on how you can handle it. It's a major problem with full-timers now. Good luck. There must be a way around it. Hopefully, someone can chime in.