To determine if the tree will survive, it is important to determine if the rabbits have damaged the cambium layer (food-conducting tissue) under the bark. If they have girdled the tree or eaten and damaged the tree all the way around the tree trunk, there is no way for water and nutrients to get from the roots to the leaves and the tree will die. If only about 25 percent of the cambium or trunk is damaged, the tree will probably live and leaf out. It will be under stress and you will have to water the tree to compensate for the lost water-carrying capacity. If 50 percent of the trunk is damaged, then the heartwood is exposed and the tree becomes susceptible to other damage and will most likely die.
Protection from rabbit feeding damage is as simple as putting a tall (at least 18 inches), loose-fitting plastic tube around the tree trunk. You can also construct a chicken wire cage around the trees to exclude the rabbits. If you would like to see more information about rabbit control, Nebraska has a good publication at: Prevention and Control of Rabbit Damage