I have been there in Oct and Nov. The closer you get to January the more chance of cold fronts, although they can pop up at anytime.
There are excellent bargains to be had at some of the better lodges that time of year since it is not peak season.
I would reccomend Turneffe Flats. The culture at Ambergris is geared towards tourists while Turneffe is more of a wilderness destination. There will be less tarpon at Turneffe but more and bigger bones and world-class permit. The secenery and wildlife is incredible too.
PM me if you want more info.