Great news on the booking
We were there from Thursday 1st to Sunday 4th January this year, it was busy but I would say slightly quieter than July/August, and as French schools went back on the Monday it was noticeably quieter on the Sunday compared to the previous days. So it should be quite manageable on the Sunday, and I would guess pretty quiet on the Monday of your trip.
It was cold, I wore tights under my jeans, and plenty of layers on top, hats, gloves, etc. Think it rained but not much, that will always be pot luck!
I don't think Christmas events have been released yet but last year there was the Christmas Cavalcade, the Christmas version of Dreams! (good but not a patch on standard Dreams! IMHO), the characters in Christmas costumes, the tree lighting ceremony and of course snow flurries on Main Street.
Christmas season at DLP is fab and if you get too cold you can always just pop back to the hotel to warm up