This is our 4th year arriving on New Year's Day. Don't expect thin crowds until after the weekend, from the 5th on. Things do slow down considerably after New Years, but you will still have lines and will need to use Fastpass for the most popular rides. The good news is the parks are open late, especially MK, open till midnight Thurs, Friday and Saturday and the weather looks like it will be nice, 70's in the daytime and 50's at night. Normally the weather turns freezing for New Year's, we've never even worn shorts in our past 3 January trips!!! Disney's value season always begins on Jan 1st, but this year they did offer discount codes for everyone and really cheap rates for FL residents and AP holders. You will see lots of us checking in on the the 1st!!
Have a great trip!!