My first concern is the safety of the child. Others can speak more to positive experiences and confidence building.
The child needs to be strong enough to control the horse’s head and neck. Or a pony, if that is the size.
I know of children’s riding programs that expect riders to be able to control horses that don’t take children younger than 11 because before then they just aren’t strong enough, in the experience of those instructors.
When younger children ride, there is more longe-line and lead time as they learn and gain strength.
Also consider – Whatever size equine is used as the starter mount, unless the child is being held on board, some day there will be a fall from that height. Even with a helmet, what are the consequences to the child? It’s horses. Falling is inevitable, although hopefully rare. We hope a very small child will bounce, but who knows. A pony is closer to the ground than a horse.
Certainly plenty of young children ride ponies and horses. But “ride” can be a flexible term. If strength and control are issues, a lead rope or longe may have an adult on the other end. Child is still riding and learning body position, the horse’s motion, posting, even cantering. And as much steering as they can do.
Another factor to consider is an enclosed riding space, such as an arena with a closed gate. I cannot tell you how fast even a copacetic schoolie learns to dodge out of that gate when a child is on board who isn’t strong enough to haul him back onto the line of travel. Horses and ponies will take children across the ring to the gate. So a smaller arena is also a better place to ride, even with the gate closed, just to reduce the area of control. Open spaces with no fences are even worse, nothing to stop the horse from heading to the barn.
A local riding school just had a serious accident with a 6-yo child when the instructor did not close the arena gate. The first time the horse took the child rider out of the arena, the instructor shouted and insisted the child ride him back in, which eventually she did. The second time (a few minutes later) the horse left the arena at a canter - the child had never cantered before. Horse cantered down the paddock lane to its own place and slammed on the brakes, unloading the child into the fence. I don’t know the exact injuries, but the child was in the hospital for several days before she was walking again. Child does not want to ride a horse again, and I don’t blame her.
Make it a rule for your child’s riding: If a young-child-on-equine is in an arena and not on a line, close the gate !!! Make that non-negotiable for any child who doesn’t have the strength to stop a recalcitrant horse.
Close the gate even with a child on a longe-line circle, because some horses will drag a longe line out of the gate.
And horses don’t tell you ahead of time “today is the first day I’m heading out the gate!” lol