Florida weather is so weird that you can never tell, but it is usually chilly (not cold, but chilly) the begining of January. As for the park attendance right after New Years Eve the attendance drops dramatically all the way through Februrary. This year New Years Day is a Saturday so I would say as early as Monday January 3 you should see a considerable drop in park attendance. Don't know about resort discounts, but you can always ask...I know the cruise line starts their discounting that week, so resorts might have some good offers.