My husband and I booked a last minute cruise 2 weeks ago (January 7-10) and I can definitely second your thoughts on the weather, OP! It was on Majesty out of Miami. We also had not-the-best weather. When we arrived in Miami, it was maybe 50 degrees and windy, although sunny and beautiful-looking. Day 2 was supposed to be Cococay but the water was too rough for the tenders to get to the ship so we weren't allowed off the ship and headed straight to Nassau instead. We got into port there at about 630-7pm and stayed there until 4ish-pm on Day 3.
It was so windy on Day 2 that people were walking around the pool deck with hoodies and jeans on. The midnight buffet by the pool was chilly also.
Day 3 in Nassau was the best day of all, weather-wise. It was about 70 and sunny. Although a lot of the shops were closing early in the day so it was not the best day to be in port there, if you were interested in shopping there. We have been there 4 times now and I have no desire to go back, really.
We have cruised in the winter 3 times previous to this trip and usually have great weather.
Majesty of the Seas - Jan. 2011
Majesty of the Seas - Feb. 2009
Sovereign of the Seas - Feb. 2008
Majesty of the Seas - Nov. 2007