My daughter was two years on the Mississippi Gulf Coast (Keesler). I found November and December good times to visit. It could be cold at night, seldom freezing. It could be warm enough for light jackets during the day, feeling really nice if the sun is shining on you. Sunny days, northern visitors might even go to the beach. They might not always go in the water. It will not be summer warm, best you might expect is a like a mild fall day up north, October weather in December.
Attractions, Gulfport to Mobile, stay open year round. There are the parks for exploring nature, malls for shopping, casinos. I don't know what other attractions you might seek, this is not an area big on theme parks and such.
The bummer for me was that the storm systems we enjoy Spring and Autumn on the southern plains, and all summer in the upper midwest, move down to about the level of I-10 and I-20 for the winter. On a cycle of a week to a week and a half, there will be a few days of cold, often heavy rain, follwed by a few days of sunshine. The rains tend to come with some pretty heavy winds, and when Arctic air masses push down into the southern states, this will be Winter's Tornado Alley. Such events are rare, but pretty miserable if camping.
All things considered, in December I would rather be on Florida's Natures Coast (north ot Tampa to the beginning of the Panhandle) or on the Texas Gulf Coast or Coastal Plain, somewhere from Houston south. That seems to be more out of the weather patterns that run across the mid-South and lower South during winter. Not so bad if you have a house, but the stormy days will be a problem for camping.