I'm curious on this as well. I always had the theory that January would be the best time to go on a cruise! Take a week out of Winter and replace it with Florida/Bahamas. Plus cruises seem to be cheaper in January.
Not sure what the weather will be like in the Bahamas, but we did do WDW in January one year. The week before the weather was forecasted to be 60s. Two days before we left a cold front came in and the weather changed. It ended up being high 40s. It was COLD. It sleeted one morning actually! I had to buy gloves in the park actually. Going out at night was tough because the sun was gone, so we doubled up and layered up as much as possible.
That said, I get the feeling that is not the norm at all. I think the best thing to do once you book is watch the weather very carefully a few days before. That was what saved us. I could tell when we were there families had not been paying attention to the weather and were stuck in shorts and tank tops in the 30 degree weather. No fun.
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