Sebaceous or fatty cysts are a common medical medical issue in humans and dogs, but less so in horses. Nevertheless, they are not unheard of, and veterinarians are trained to deal with them easily.
A sebaceous cyst is a bump beneath the surface of the skin, filled with a fatty, white pus called sebum. The term is used fairly interchangeably with epidermoid cyst. While the two cysts differ in their origin (an infection of a sebaceous gland versus that of a hair follicle), they are treated the same.
A sebaceous cyst that forms in the nasoincisive notch (false nostril) of a young horse, atheroma is a painless lesion. It rarely grows large enough to impede the flow of air into a horse's nose, but is generally removed for cosmetic reasons.
Sebaceous cysts can be removed easily by a veterinarian. Local or general anesthetic can be used to calm the animal, and a dorsal or ventral incision can be made to remove the cyst. After removal, the area is sutured. The dorsal incision is easier for a vet to do, but the ventral incision is less likely to leave scars.