Great waterfowling, fishing, weather, dove hunting and not far from Mexico where dove hunting is super. But trap...not much. You won't find near as much trap in this state as in some other states...especially the midwest and eastern states. If you are a "games" shooter...almost none in TX.
Try Corpus Christi/Rockport area. Lots of snowbirds, great saltwater fishing, active gunclubs at Corpus Christi pistol and Rifle Club, and Victoria Trap and Skeet Club. Some of the best Bird hunting in Texas. Corpus has big 50 shoots year round.
As a retired meteorologist let me suggest you pick out a couple of the larger cities in different areas and check the average temps, precipitation, etc before you commit to Texas especially if you think the weather will be mild in the Winter.
I dearly love Texas having lived there several times while serving in the USAF.
There's an old expression about Texas --- basically north of Austin --- in the winter time the only thing between Texas and the North Pole is a couple of barb-wire fences --- it gets cold, cold and windy, windy.