I'm not certain what that is exactly, but i believe it is a bird. Probably some sort of owl. Try a birding website to get the exact species. The repetitive nature I heard and you described does not sound like elk. If it were some sort of small mammal, like a squirrel it would not continue all night. So like I said, best guess is its an owl.
UPDATE-because I'm a geek and it was eating at me- I'd now say it is a northern pygmy owl, given your location and the owl calls I was just listening to.
Winter is tough on whitetails, that is an accepted fact.
You can help the quality of your herd by providing winter plots - that are not necessarily designed as kill plots.
Having what I call green plots - that the deer can browse in when most of the other food is gone, can greatly benefit the deer herd when they need it most.
Come December - at least in our area of the south - most of the mast is gone, all of the crops were long harvested and this green browse can really make the difference for...