The year we did the season we arrived the 26th. Magic Kingdom was busy but not unejoyable. The only day they closed a park was New Year's eve... MK closed close to noon. It was packed, unbelievable! Everyone wanted to see the fireworks. We just turned around and went to AK, and it was fine there. And after NYE the crowds shrunk considerably.
The weather was quite warm that year. Sweatshirts in the evening, plenty warm enough to swim during the day, DH & DS even went to a waterpark... but it can be anything. Last year we were there the first week of December and it was freezing! We wore coats, hats and gloves at night and were still chilled. Swimming was out of the question! That turned out to be the coldest week of the whole winter... you just never know so pack for anything! But warm, cold, or crowded we still had a wonderful time!
(FWIW, I packed one of those silver disposable blankets -- we used to call them 'space blankets' -- in my pack when we went last year. I didn't expect to use it and did think it would help much if I did but they take up almost no space so I brought it along. It was so cold one night I got it out, and boy did it help against the cold wind! We also put in between us and the cold sidewalk during the parade and it helped a lot! You can find them at Target, they are right next to the rain ponchos.)