If a tree is girdled (the bark stripped off completely around the trunk) it will die, since the inner bark/cambium layer is the living part of the tree that contains the veins of the tree (phloem) that transports the sap from the leaves to the roots. (Well, that's a bit simplified and not exactly precise but you get the idea.)
I'm afraid it doesn't look good for your trees.
Rabbits as well as deer, mice, and other foraging animals will chew on the bark during winter. It's best to protect them by wrapping the trunk to the base with hardware cloth or specific products sold for the purpose.
I discovered yesterday that I neglected to protect one of my blueberry bushes and it's been pretty severely "pruned" (in this case they like eating the tender/twiggy branch tips)
. I was going to scrounge together a hardware cloth or a wire fence cage for it today, but the little blueberry bush is now under 18" of snow!