I have been to the Bahamas several times on cruises in Jan and Feb. Its about a 50-50 chance of it being beach weather. It will be pleasant for walking and shopping . It could be in the 60's or 80's. Just have to be lucky.
We were in the Bahamas last year on dec. 30 and the temp. was 85 deg.
Carnival Liberty New Year's Eve 2007
Liberty of the Seas 5/2008+11/2009
Allure 1/16/ 2011
Independence of the Seas 12/29/2013 Top-notch!