that depends on your area as far as the flow, and the stores the bees have, AND the type of bees you have.
I leave the supers on until the goldenrod flow is done, which , is about any day now.. then pull the supers.. "I" get what is in the supers.
I do not touch what they have stored in the brood chambers I left on.
I know some beeks that take every drop of honey they can scrounge, and then feed syrup like crazy to replace it. I don't like to do that. I feed 2/1 syrup, but its only to supplement what they have, not replace it.
I am also switching to all mediums, but still have some deeps.. so I leave two deeps, or three mediums, and let them backfill with the remaining nectar / pollen in the area for a couple of weeks, then start feeding 2/1 syrup AWAY from my hives with a bit of honey-B-Healthy.
I know ppl say outside feeding causes robbing.. But putting a few feeders out about 60 - 80 feet from the hives HAS in the past almost instantly stopped any robbing. It is ONLY my theory that it gives those robbers something else to focus on, and or reduced the desire to risk their lives to rob when something good is available so close.
I do a check on the hives before winterizing to see how well they did, and try to make sure they have full stores. Every frame filled with pollen/honey/syrup. Adding back the frozen frames etc. I make notes which hives are best off, which seem a little light.
I winterize and leave them alone until... Say, Mid January we get a 50 degree + day that is sunny.. even here in Iowa that does happen. One January my wife and I were horseback riding and it was 67 degrees. Sometimes we dont get a good day like that until early March. Sometimes we DONT GET a decent day, in which case I have to watch the weather and PICK a day and go with it...
I pop the inner covers and look to see where they are at. If they still have stores I put the cover back on and leave them alone. If they are in the top box and stores are low, I put newspaper on the top bars and pour granulated sugar on it. then cover it up and leave them alone.
My Italians usually need sugar. My Carniolans are 50/50 sometimes they do, sometimes they dont. My Feral bees usually come out of winter with excess stores.
Some people use candy boards through the winter.. I tried it, and apparently dont have the necessary cooking skills and ended up with a mess. There are recipes out there for making boards with out cooking the sugar mixture.. but, I dont see much benefit to those over the granulated sugar. I like the moisture absorption of the granulated sugar.
Everyone does things differently, everyone has their own tried and true method. Figure out what you like, what you are comfortable with and go with it. Beekeeping is a learning experience, its heartbreaking, and its thrilling. It is expensive at times, and its rewarding at times. When you do something that fails, and you lose bees, it hurts, but dont let it make you quit, let it teach you not to do that again, and the painful reward of that is, you just learned, and got better.