I was on the Majesty of the Seas this past January (end of January) I was on the 3 night cruise and we went to CoCoCay, and Nassau.
The weather was too cold to enjoy the pool on the ship. We did sign up for the snorkel package at Cococay, but the weather was too cool for us to go in the water, so we skipped the snorkel package and instead relaxed on the beach. (sun was warm, not hot - air was chilly)
We had a great time overall, the ship was great, but we felt that the weather was a bit too cool. (not cold, just cool)