I spend every winter on Little Cayman and am out diving every day. The water temperature in January will probably be about 80F, but it could be as cold as 78F or as warm as about 81F. In any case, I always use a 3mm full suit. I have two of them--one much better made and tighter fitting than the other, which makes it a little warmer. I actually prefer the cheapie, because it keeps me warm enough and is easier to get on and off.
You will see some people wearing a 5mm suit, but I really think that's overkill. And I do remember one DM who always wore a 7mm suit in the winter. I thought that was absurd at the time, and still do. On the other hand, I'm a little skeptical of shorties, though that's what you'll probably find the resorts have in rental. If it's warm enough for a shortie, I would opt for a 1mm full suit instead.
Bruce