I am super temperature sensitive as well.
For me, January is the best time of year. Having said that, *if* you plan on going in January, and *if* you are using a mobility device, plan ahead. The biggest problem for me in January is night time.
The evenings can - and do - feel chilly, especially by the water, and on the boats. Additionally, the movement of the mobility device as you drive can actually cause you to feel colder, because there is a wind chill effect. People who are walking usually don’t notice it as much, because they are active.
I take along clothes that I can layer (lots of light layers, so that I can put on more if I get colder, and take off layers during the warmest part of the day) as well as a warm scarf that I can put around my neck, and pull up over my head if needed. I also take along warm, lightweight gloves; my hands get SO cold! Needless to say, I have a blanket folded across the seat back of my wheelchair as well.
I also take along lots of the little “hot hands” packs; I have found that the smaller size is great, because I can put it in my pocket, or even in the palm of my glove, or tucked inside my shoes if my feet get cold. I have zero shame when it comes to staying warm; I have been known to tuck these ALL over! LOL
The great thing about January (besides the Art Festival at EPCOT) is you can still have those lovely, warm sunny days where you can soak up all the warm, and then sit in front of a roaring fireplace (thinking here of Wilderness Lodge) and enjoy a nice warm beverage in the evening!