If in doubt, call on your vet - owning a horse is expensive and we must expect to pay out for vet visits at times. However, the best advice I can give is don't panic. If the cuts do not look deep and if the bleeding is not profuse, the first thing is to clean the wounds. Your horse will not appreciate this so be sensitive. hose his wounds down with cold water. If he is still bleeding, this helps stem the flow of blood. It also helps reduce swelling as well as cleaning the wound out. Run your fingers gently over the wounds, being alert and expecting a reaction. Make sure there is nothing embedded in the wounds - no grit or dirt.
When you have cleaned the wounds, you will be able to judge whether they are deep enough to need a vet. If you feel there is no muscle or ligament damage (watch out for limping) then you can apply a special dressing to keep the wound clean and free of infection. Check whether your jabs are up to date at this point - tetanus is a must and if it's not up to date then you must call the vet.
Keep an eye on the wounds, resting the horse for a while. If all is well, the cuts should heal within a few days. bathe the wounds daily and apply the dressing as directed.