The barn I am at will use spray on farnum scarlet oil for cuts and abrasions. It's a good antiseptic. They use the scarlet oil for a few days and while the wound is wet and when it begins to scab over change to fura-zone to promote hair growth.
I find I get quicker results and hair growth with fura-zone on nicks, bites, hair loss areas than just leaving it to heal on its own.
We recently had a horse remove the entire hide from his two back legs while entangled in a fence. The scabs have healed and the flesh is appearing normal.
Take care for sunburn on the wound. If the hair is gone that area can be susceptible to sunburn.