The Gulf Coast during the winter is often chilly except for the coastal areas of southern Texas and the lower two-thirds of Florida. I have some friends that have stayed in a condo in Gulf Shores, Al for the month of February for about 4 years and they've seen down right cold to cold & rainy to mild. I've stayed in Corpus Christi, TX in late January and had mild temps, but windy.
Late February and March will be busier along the Gulf, especially March. We usually stay in Florida about 70 miles north of Tampa. It's cooler there, but generally mild. Our campground is often booked for many days in February with occasional vacancies. You should find available campgrounds along the upper Gulf Coast in January and February mainly because it's too cool for many snowbirds.
You might spend some time reviewing average temps for areas along the Gulf. Below is a Weather.com site with maps of average temps for the U.S.. You can check specific cities too.
http://www.weather.com/maps/averages