Thank you for the question. We are sorry that your tree suffered so much damage this winter. I can't tell if it's been girdled all the way around so it's hard to say if it will survive or not but it does look like it has been quite compromised. Completely girdled trees usually leaf out in the spring by using food stores from last year but soon run out of "fuel" and die. Extremely, but not completely girdled trees may survive and we all know cases where this has happened, but it will be more susceptible to drought, cold injury, and insect and diseases infestations. If you decide to remove it, please read our publication on how to protect your trees against winter animal damage in the future: http://www.extension.umn.edu/garden/yard-garden/trees-shrubs/protecting-from-winter-damage/
If you decide to nurse it along, be sure to water regularly and fertilize it to give it the best boost. Good luck.
Thank you for contacting Extension.