We have been there at this time many times and to be honest, it's always different based on when school goes back and what day of the week it is.
One year, Jan 1 was a Sunday and the parks were practically empty. Many schools started Jan 2 or 3 that year. Other times the crowds have stuck around through the week. That is a very inconsistent crowd week IMO based on our experience. NYE is obviously always bananas, but NYD and following has really varied for us.