I will be on the same cruise 1stTimer!
This is my first January cruise so I can't speak from experience, but I found this thread in the Cozumel board: http://www.carnivalconnections.com/cruisetalk/forums/t/82702.aspx that addresses winter cruises in that area. From the cruises I have been on (in October and in April) I think that the sun will warm us plenty, especially once we get out into the gulf and towards Mexico.
Ecstasy, 1/2010
Conquest, 10/2007
Conquest, 4/2006