I agree with all the above. We've been in early February, but not January.
One year it was supposed to be in the 70's the whole trip. I didn't pack a sweater, sweatshirt, or jacket!
Well you can imagine how cold I was when it was 50's and cold!!! It felt colder than our Minnesota weather at 50.
We looked all over WDW for a sweatshirt. They had those thin hoodie things, but no "real" fleece sweatshirts anywhere. Florida's idea of a sweatshirt and Mn. idea of a sweatshirt are completely different. We don't care if they are cute, just so they keep us warm. My husband wore a sweater on the trip down, and I ended up wearing that sweater for 4 days in a row!!!
He said he was warm enough in his regular shirts.
What a guy!
So, don't let the forecast fool you.
One funny experience that happened in the MK on a "cold" day in they low 60's. We were without jackets, sweatshirts. Just had on normal t shirts and jeans. We went to Tomorrow land, and one of the CM's had on a bulky, down coat with attached hood up. She had a beanie on under the hood. She had a scarf, gloves, and boots on, and she was STILL freezing. I felt so sorry for her, but it was kind of funny to see (reminded me of Kenny on South Park, LOL).