our bees are in Europe as are yours, only more to the south - in Slovenia, home of the Carniolan bee strain.
In my view bees are like hamsters, they will keep accumulating food until they run out of space or out of harvest.
You don't have to remove all the honey that you judge to be surplus just because of the honey itself. The really good reason to remove full honey boxes (apart from the one above the brood) is to shrink the volume of the hive so it's easier for the bees to keep it at a sensible temperature over the winter, especially in your harsh climate.
But don't just mechanically remove boxes - always check where the colony is really located inside the hive because sometimes the bees will move a box or two up from where you would have expected them to be.
When there is sufficient honey in the hive you don't absolutely have to feed sugar. A lot will depend on how things to in the spring. If there is a too early warm spell the bees might wake up and start using up the stores at a faster rate while there's nothing yet out there to harvest. At that time, if they start running low, it would be a good idea to add sugar as cake or even just as dry sugar - OR you could have some frames full of honey from the previous year which you can "plug in" as needed.
While the honey option is great, it's a good idea to know which frames came from which hive - for sanitary purposes, to avoid any disease spread.
At our location we mostly feed sugar with some protein in August and early September because at that time, the winter bee generation is being created and there absolutely needs to be enough carbs and pollen - and unfortunately there usually isn't enough in nature. Only after mid-September do we have abundant crops of buckwheat. So there's usually no problem about having enough food over the winter BUT if we avoided an artificial food boost during late summer we just wouldn't have enough winter bees to carry the hive into the next spring.
When you perform anti-varroa treatments at such low temperatures (you mentioned 2 C), may I suggest oxalic acid in a sugar drip, applied by syringe on top of the winter "ball" of bees - it's worked wonders for us regarding varroa control. Google around for dosage and optimal temperature for your area; here we usually do it shortly before Christmas when there is usually a relatively warm spell (10 C-ish) so bees can fly out the next day to clear up their bowels.
I hope some of this wall of text can be useful to you