Our favorite time to go is the first or second week in December - you will love it if that is when you are going!
You have to be prepared for any kind of weather. I have been so hot I was sweating at night and I have been so cold we were shivering! (Really, I am not exaggerating

)
Usually, it is somewhere in the middle of these extremes, but you have to be ready.
I suggest carrying shorts and long pants; t-shirts, long-sleeve light weight shirts, sweatshirts and gloves. If it gets really cold, you just layer. One year as we walked around EPCOT it got colder and colder! Every country we came out of we could tell a difference. It got down to freezing that night. That year, we wore a t-shirt, a sweatshirt AND a jacket! But we had a blast and that may be our best trip yet! The next December trip we wore shorts and t-shirts to
MVMCP and I remember literally sweating! We did NOT want the free hot chocolate!
SO! Just be prepared for everything. We've never carried overcoats, only light jackets with plans to layer if necessary.