If you cruise in the Caribbean, you will probably go to Cozumel, Mexico. Tourism is Mexico's best money maker, and they are glad to see you coming.
Carnival Cruise Lines have been going to Cozumel for more than twenty years, and now have their own dock. The day we were there last week, there were three Carnival ships in their dock and two other ships at a different dock a few miles away. The Carnival dock is about three miles from downtown, but you can get a taxi for only $5 if you want to do some shopping. (Leah and I were riding in a taxi there several years ago, and I kept asking the driver questions, and he kept ignoring me. I suspect his English skills were limited or nonexistent. Or, he might have been having a bad day.)
We have been on several different excursions out of Cozumel, so last week we just stayed on the beach near the dock. There is plenty to do there; lots to eat and drink and many vendors with things for sale.
I have been to Cozumel in all four seasons, and it is always warm and breezy by the water, and always hot if you go inland. I'm thinking it would be a lovely place to spend the dark days of February.