Since we are gardeners and not horse experts, we had to go hunting to find some answers. Everything we found seemed more concerned with why the horse was doing that, and not what the result is on the tree. Mostly, the opinion was that the horse was bored or needed more fibre in its diet.
If the tree has been completely girdled; that is, if the bark has been cut in a complete circle, the tree is going to die. In fact, girdling is suggested as a way to kill an unwanted tree witout use of chemicals. Complete girdling cuts off the food supply from the leaves to the roots. Sometimes suckers will come up from the roots as the tree tries to save itself, but not all trees sucker readily.
Since your question was how could you save the tree, and we don't know if it was completely girdled, we found this article from New Mexico State University Repairing Damaged Tree Bark. It sounds pretty complicated, so you may decide to just let Nature take its course. If the tree was not very big when it was damaged it might be easier to just replace it, but we would certainly recommend you not rent to horse owners again. From that article:
"The reason for damage due to girdling is that the phloem layer of tissue just below the bark is responsible for carrying food produced in the leaves by photosynthesis to the roots. Without this food, the roots ultimately die and cease sending water and minerals to the leaves. Then the leaves die. As you can see from this process, there is a delay period before the roots and top dies. There are some stored foods in the roots and lower trunk that allow the roots to continue functioning for a little while. This delay gives you time in which you can try "repair grafting". Don't wait any longer because the roots will soon run out of food."