Although not common.. whitetail will still breed into January and even into February here in the midwest as fawns enter into estrous. It will not be a full out rut like is seen in November.. but it does happen.
Also.. whitetail do dig through the snow to the earth below looking for food that is beneath it. It is not uncommon for them to dig a little into the dirt and even eat some of it.. taking in some nutrients like salt.
Hope this helps some good Doctor..