Yes. However, deer look for twigs, berries, and other food items that are above the snow. A deer must burn a lot of energy when it digs through the snow, so it tries to avoid doing that. Of course, this animal will dig for food in the snow before it lets itself starve.
An older deer or one that is ill may not have the energy or strength to dig through the snow for food. This is why many older ones die over harsh winters.