If it's the 7 day you should be fine, but the 3 and 4 day only go as far south as nassau and it can be very cold there in Jan. , but doesn't stay cold. Unfortunately for us, the folks returning the day we sailed had 3 beautiful sunny warm days . Ours was 4 day and we froze at Port Canaveral,Nassau and day at sea. Our day at CCay was perfect, and we later heard the cruise to Nassau after ours had perfect weather. I guess I'm saying it should be okay , but you are taking a chance if it's a Nassau cruise.
You can get some great rates at this time of year.