Unlike many couples who have holiday weddings in cold, snowy places you may have more choices available when it comes to venues. I say this because beaches in certain locations may not be as crowded in December as they would be on warmer days.
On the other hand, people who choose to vacation in the tropics at the holidays, may fill the venues you'd like to book.
As with any wedding, be sure to start looking for that special venue early.
I can speak from experience about the state of Florida and tell you that in December the central and northern Gulf Coast areas can be quite cool at that time of year. The water temperature has also dropped by then. That means that the beaches themselves will be much less populated, if you want to stand on a beach and exchange vows. However, when I lived in central Florida I thought that December was one of the best months to be outdoors.
Florida even has a place called Honeymoon Island, which accommodates weddings.
If you want hot, balmy weather which includes warm water swimming, better head farther south to the Florida Keys area, islands of the Caribbean, or take a cruise.