Two things comes to mind...
Even when there is deep snow there is usually enough wind to make some spots bare, or not nearly as deep, so the deer can still access the corn, etc, in a given field.
With the snow piling up last night I saw deer up on their feet actively feeding at least three separate places on the way home from work last night. Two of those places were right in the ditches along the interstate. I could see them actually pawing the snow away to get to the grass/clover below.