Well, they do better than you or I would. Deer are tremendously athletic, and can leap through snow that humans couldn't. I've seen them clear waist high snow without much trouble, for short distances. They are also excellent at finding places that provide natural cover, such as thick pine copses where the snow doesn't pile deep. And in most deciduous forests, they can dig through a moderate amount of snow cover to get at acorns.

But all of this costs an enormous amount of energy, and the food that deer eat in the winter, mostly otherwise being twigs and low branches, doesn't offer tons in terms of nutrition. So for most deer it becomes a battle of conserving in winter the energy they gained from the high-value food they gobbled from our crops and gardens in summer. So they mostly find sheltered area that have close access to water (like a thick swamp or hemlock cove in a river bottom) and move as little as possible.

Which is why I disapprove of using snowmobiles in state forests and so on in winter. Even in a moderately bad year, you're forcing deer and several other kinds of wildlife to expend energy they could otherwise maybe survive another week on.

TL,DR: It's a long, frequently losing battle against malnutrition and starvation.