The horse is not lame, but seems stiff and is tender when you examine the area. If the puncture is not bleeding and no tissue is visible, use a Q-tip to check its depth. If there is bleeding, apply pressure using gauze squares, bandages or clean towels. If tissue protrudes from the wound, do not remove it. Initially, try to clean or flush uncomplicated wounds with clean fluid.
Sterile solution is best, and many contact wetting solutions work well.
Avoid putting thick, sticky ointments or sprays on the wound. They make it harder to fully clean the area. A spray bottle can be helpful in forcing hair and dirt out of a wound, but be careful in dealing with punctures. If you feel cleansing will push the debris in farther, leave that job to the vet. In the case of puncture wounds, always consult your vet.