Depends on which months. Dallas is usually still nice (just cooling off enough to be nice for people accustomed to northern summers at beginning of October, can be having ice and snow by end of November, but mid-December is more typical.
San Antonio starts getting cool in November, has occasional cold days in January and February. The rainy season starts in November, and though it gets below freezing from time to timein January and February, frozen precipitation is rare.
Spring is March in both places, San Antonio will be getting warm to stay warm, Dallas going back and forth between cold and warm as fronts come through, with Tornado Alley weather.
Whether either works for snowbirding depends on your expectations. North Texas weather is so little different from NW Arkansas, southern Missouri, NE Oklahoma, that I might as well stay at home. Some snowbirds spend about 4 months here, going further south only for Jan-Feb.
San Antonio works for me in the two coldest months, I would go there in winter when my daughter lived there, but if you are expecting anything like summer weather, you need to go a lot further south. No place in south Texas has winter weather anything like that in South Florida or Southern California, which is why Texas is a less costly place to rent a patch of land for the winter.
