I used Punchy salve on my horse's hind legs when he had skinned them on a fence.  I didn't see the injury for a few hours and it was -25C so frost bite was also an issue.  Fast forward 3 weeks after using the salve and bandaging, and the hair is already growing back. 

Your unicorn is going to hurt itself!  I'm using Punchy Equine Wound Salve because it's 100% natural. The qualities of Pine Sap have been used for centuries and of course, it works!