The carribean is warm and comfortable either time, but in December you may run into El Norte winds that kick up the surf and sometimes close the ports to small boats. I've been to Cozumel and Belize in November and February and only wore a dive skin. My last cruise to Cozumel in November, the wind and waves were rough and all water excursions except diving were cancelled. Despite the rough boat ride, it was fine underwater.
I recommend Dive with Alison in Cozumel. She works well with cruise people. I've heard of people who booked through the ship and the excursion got cancelled at the last minute due to a lack of people.
Last time in Belize I went with Sea Sports which was fine, but very tight on the time and we almost didn't make it back in time. You have to take a long tender ride in Belize to get to shore, but if you dive with the ship, the diveop picks you up and drop you off at the ship. Next time in Belize I'll dive with the ship. There was no time in Belize to do anything else, but it's not a port you really want to walk around. It's considered dangerous, but they do have a fenced in port area with some souvenier shops and restaurants. The cave tubing is a popular excursion there, but I hear they take armed guards along.
Costa Maya was hit by a hurricane but has rebuilt. When I was there I took a cab ride to Majuahual (spelling) and it was great. Rustic mexican beach town with open air hut restaurants and bars on the beach, $25 1hr massages on the beach. I saw dive signs in huts on the beach. I think you can hire a small boat to run you out to the reef and perhaps just swim it. I did a boat snorkel trip with the ship because my niece was with. The seas were kind of rough and she wanted to quit early so we didn't see much.
