The only way to figure out if a place is for you is to go there and try it out. Some people love the Texas Gulf Coast in winter, others describe it as too cold, or too windy, or too wet, or a combination of the three.
I prefer Port Aransas to Rockport, and the Gulf Coast to the Rio Grande Valley, for atmosphere and the opportunity to do things that interest me. Others prefer Rockport, or Corpus Christi, or Houston, because their interests and needs are different. But all in all, I'd really rather winter in San Antonio, because I find it warm enough, like the multicultural atmosphere (which terrifies some people from culturally homogeneous places) and I like the services and activities available.
So go down, move around, check out different places in Texas, find what suits you.. While you are at it, don't miss checking out west Texas and SW New Mexico, From Davis mountains and Big Bend, over to White Sands and west. These places have their fans too, and have not yet turned into snowbird ghettoes. But a lot of people like the snowbird ghettoes too, as a community of "people like us."