In winter you can carry a lot more with you because normaly you have some kind of jacket with plenty of extra pockets. You also need to think about if you needed to get home and how cold it might get. A few things that you could add to your Winter EDC:
-Emergency foil blanket
small compact and keeps you warm, at least its the smallest blanket that I could come up with.
-Scarf or Bandana
covering your throat really helps keep the warmth in. Scarfs or banadas can also be used for: bandages,slings,to tie things up, head wraps, to filter water after being boiled.
If your hands are freezing, its hard to do much of anything. You not going to be able to flip out your knife or other weapon quickly if your hands are like ice.
Those are the 3 most important winter EDC items. Of course some kind of weapon depending on the legality in your area, or if you have to go to work or somewhere else where it is not possilbe to bring a knife or gun.