Yes, do remember the Gulf Coast isn't in the tropics. They do have winter, just a much milder winter than places to the north.
You will still need sweaters, sweatshirts, long pants and jackets. But you won't likely see freezing weather often.
Have to pay attention to the weather, and be ready to go through the occasional (once or twice a winter) cold spell with a mild freeze.
One bit of advice. If you do happen to be there for one of those very rare occasions with snow and/or ice - don't go out driving. You might know how to handle the conditions - but no one else does - and everyone will be out to 'enjoy' the experience.