If that damage is all the way around your tree, it most probably will die.  It looks like they have chewed deeply into the trunk cutting off the flow of nutrients up and down.  I am impressed that you fenced it off.  That is what we are supposed to do.  However, as the snow got so deep this year, a second fence up higher would be have been needed or at least a plastic sleeve up there.  You tree will probably leaf out and may even bloom using stored energy.  Watch as the season progresses to see if it starts to fail.  Sorry.  It is so frustrating.  It looks like a lovely tree.  The dogwoods and lilacs can send up new stems.  Just remove the dead ones at ground level.