I have never used silver nitrate to cauterize anything on a horse, but I know they are still using it on people. It's pretty impressive to watch at work, but there is no sensation.
We were caring for an acutely disabled teenage boy whose g-tube stoma was not healing well and the doctor had us use the silver nitrate sticks. They really worked to clean up the wound.
But as Dr. Heidi suggests, let the vet determine appropriate treatment.