You can treat superficial wounds yourself, so long as you stick to some basic rules:
Cleanliness is the be-all and end-all of horse wound care. Beusker: “Ideally you should wear disposable gloves, or at least wash your hands before you treat the wound.” Iodine solutions and compresses, for example, are suitable for carefully swabbing wounds to the horse’s skin. Another tip: “It is recommended that the hairs along the edges of the wound be clipped or carefully shaved to prevent them from sticking.”
Keep the wound dry but hydrated: if you have just disinfected the wound, dry it with a clean towel before applying a specific cream that will serve as a barriere against germs and bacteries.
In some cases, applying a bandage can help it stay clean and safe from infections, if you don't know how to do it, don't hesitate to call your vet.