Sorry I think I have to disagree with many responses here.
The response should be to understand better how much honey a colony needs to survive through winter. If you have local mongrel, Buckfast or an English Black Bee then it is generally reckoned you should be okay with about 40lb of stores. If you have the Italian Bees - yellow then you may need more as they can be quite prolific.
So you need to check how much stores are in your hive, now a full standard national brood frame, covered both sides is about 5lb, a super national frame about 3lb of honey. So how do you keep your bees, single national, double national, brood and half, Langstroth, 14 x 12 there are many variations. I personal keep my bees generally on double national, but only 8 frames to a box on the basis that bees like naturally to go up and down not side to side – that is way most trees grow. So I look to ensure my bees have 8 frames of stores leaving the queen 8 frames to lay in and in spring if need be I can give them more frames.
As for do you need to leave all honey it is generally agreed that honey does contain vitamins and minerals that either bought syrup or sugar mixed yourself does not have. However, it is also generally agreed that if you leave about 50/50 in a hive to go through winter that also works well. Why, well I will happily pay for Sugar for my bees, but then I sell my honey at £8 a pound so it far cheaper for me to give my bees some sugar to last through winter.
So yes, once the supers come off which I have done will feed until such time as the hive has 40lb of stores in it. With Ivy, a little Heather and Himalayan Balsam in my area still coming in they will pull in a mixture of my syrup and local Nectar. In December they get a pack of fondant when they are vaporized. Why well again the cost of fondant is low v what a new colony of bees cost so better to be safe and just leave them with it.