Winter is harsh on wildlife. Food sources are limited and therefore the animals energy levels are not optimal.
All winter wildlife have adaptions which allow them to survive during the lean months.
White Tailed Deer for example, enter a state where their metabolism reduces to the point where they can subsist on buds from trees.
Never feed deer in the winter unless you can sustain it over the entire duration of the cold weather. The food you feed them will increase their metabolism to the point where they will become dependent on you for survival.
You will help them much more by simply creating trails in the deep snow with snowshoes, skis or snowmobile. This allows the wild ones to move through their home territories with very little expenditure of valuable energy.
Of course, the wild ones do not need us; but since we live in their homelands, it suffices to say that helping them out by simply packing down a few trails goes a long way to making our transgressions feel less intrusive.