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My son cruised the Western Caribbean this past December. Their excursion to Playa del Carmen was canceled because of rough seas. They had cold weather in Key West. It was too cold to sit out on the deck. They wore mostly jeans and long-sleeved shirts.
I cruised this area in February and we had wonderful weather. However, swimming while in Grand Cayman, was not very comfortable. The water was a little too cold. We go to Cancun every Feb/March, and the water is cold there too.
Did a Western Caribbean cruise on the Radiance back in Dec '07 and the weather was mixed. Chilly in Key West (pants and sweater weather) - came back to the ship early and hung out in the enclosed solarium. The rest of the ports had perfect weather - not too hot and not cold in Grand Cayman, Montego Bay, and Cozumel. Actually Cozumel started out a little cool and by the time it warmed up enough for us to want to swim, we were heading back to the ship.
I think it varies, but you should be okay. We didn't get any rain the whole week on our Dec western, whereas on our 9 night Eastern in June, it rained every day except 1 or 2.
Just make sure to bring a pair of pants and a light sweater or jacket incase you hit a cooler day or 2.