Supervision is the whole system
Every other rule in this article is a backup for the first one: around horses, a child is supervised by an adult who is within arm's reach and actually watching — not across the yard, not on the phone, not assuming the pony is bombproof. Horses are large, fast-reacting prey animals, and even the quietest yard pony can shy into a child when a feed sack rustles behind him. Accidents around horses are rarely caused by a bad horse; they happen in the three seconds nobody was close enough to act.
Where a child stands, and where they never stand
Teach positions the way you teach road safety, as fixed habits. A child approaches a horse at the shoulder, where the horse can see them clearly, speaking as they come so the horse is never surprised by a small person appearing at his head. Nobody walks behind a horse — not to pass, not to fetch something, not ever — because the kick zone is exactly at child head height. Children also learn not to kneel or sit near hooves, not to wrap lead ropes around hands, and to stand clear of gates when horses are coming through, where a bunching group can swing a gate hard.
Helmets, hands, treats, and washing up
Put a properly fitted riding helmet on a child for the whole yard visit, not only for riding: most head injuries around horses happen on the ground. Treats are fed only from a flat, open palm with an adult's hand under the child's, so eager lips never close on small fingers — and some horses simply get no hand-fed treats at all, which is a yard rule, not a disappointment. Closed, sturdy shoes always; sandals and wellies with no grip have no place in a stable. Afterwards, hands get washed before snacks — a yard habit as fixed as the helmet.
Teach them to read the horse
Children who can read a horse are safer and kinder around one. Show them the plain signals: ears pinned flat and a swishing tail mean give this horse space; a horse turning his hindquarters toward you is asking to be left alone; a relaxed horse with a soft eye and a resting hind leg is the one to groom. Match the jobs to the child as well — grooming a quiet pony with an adult beside them, carrying a hay net, filling a water bucket — and keep entering fields, catching horses, and leading alone firmly in the later list, whatever the child claims they can do.
One set of rules, enforced by everyone
Yard rules collapse when each adult enforces a different version — strict with one parent, relaxed with a grandparent, forgotten with a visiting friend. Write the rules down, keep the list short enough for a child to repeat, and make sure every adult who supervises knows both the rules and each horse's quirks: the mare who guards her door, the gelding who must not be hand-fed. With KinsLe Family Sharing, a relative you have picked can open his profile directly before a yard visit.