I've seen Hares do this to my neighbours trees. A tree surgeon friend of mine told me that if the Bark is cut the entire way round, the tree will die, but if there is still some of it remaining, then it may survive. I may be wrong on this, just something I remember him saying to me.
Anyway, my neighbour, to solve the prob, just wrapped some metall sheeting around the bottom2-3 ft of the trees, so the Hare could nto get at them, solved his prob. When I say wrapped, I mean very loosely, it was about 2-3 inches wider than the tree itself.
Wexfordman