I've been there during a weekday in January - it rained a little, and Splash Mountain made me very very cold, but the crowds were very tolerable and I went on every ride I wanted. It must have been in the first week of Jan though because the Christmas overlay was still up.
Much better than going in the summer when it's Africa hot -- takes all the energy out of you.. Just check the schedule of course..
This is one of the best times to visit, if you enjoy cooler weather as I do. The crowds are lighter and you don't roast. Just dress in layers so you can add or subtract depending on what the temp is that moment.
However, do call and make your priority seating arrangements 60 days in advance if you want to dine somewhere special. It's surprising how busy the BB or Goofy's Kitchen can be.