My husband is a vet and has put down many horses with a 4-10 shotgun at the
base of the ear. There is an opening in the skull at the base of the ear, the
pellets go in and scatter around the brain, there is no exit wound, very little
blood. Quick and clean. My husband always sedates the horse first but you don't
need to. He always gives owners a choice of euthanasia solution or
gunshot (gunshot being cheaper). If an owner selects euthanasia solution the
animal needs to be buried or hauled away quickly otherwise gunshot needs to be
used.
The man who was in charge of the foxhounds at the Arapahoe Hunt
Club, which is south of Denver, would use this 4-10 shotgun method. People would
bring him their old horses to be put down and fed to the dogs. He also was
the father of Marvin Beeman DVM who is a well known equine
vet.