Normal temperatures in Nassau (and throughout the Bahamas) are in the 80's in the daytime and in the 60's in the evening throughout the winter. Of course, extreme weather patterns can push daytime temperatures down into the 50's or up in to the 100's so it's prudent to bring extra layers (a sweatshirt, a sweater, and a waterproof spring/fall jacket, should suffice) in case you need them.
The key to successful packing for a cruise is to take the most versatile items of clothing. For example, I have met a few ladies who said that they bring one formal dress (usually plain black) and accessorize it differently for the each formal evening. They bring another (less formal) outfit for the semiformal evenings. One of my favorites is to pack the knit "golf" or "polo" shirts rather than standard T-shirts. Since the "golf" or "polo" shirts have collars, they are appropriate for wear with slacks on the casual evenings, yet still casual enough to wear with shorts or, around the pool area, to toss on over a bathing suit during the day. Additionally, you might want to bring items that you can wear in multiple combinations to give yourself maximum flexibility.