Galveston in December can be tricky weather. It can by 85 degrees, it could be 50 degrees. (Heck here in the Dallas/Fort Worth area it can be those temps too) You are going to have to wait until you are a week or so out before you are going to know what its going to be like. I would say DON"T bother with winter jackets unless you are coming from someplace cold and already have them. Even if it is cold in Galveston by the second day you will be in warm to hot weather in the Caribbean. Bring a light jacket or a sweater (my wife brings a sweater in the middle of summer because the inside of the ship is too cold for her.) and you can use it inside the ship too and not just on the first day. I doubt it will be so cold in Galveston that you will have an issue for the short time you are going to be there.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013