I rode a very full grown horse at about 7 - at a riding school. Gentle giant of a horse, very popular, queue to have a turn on him rather than a pony. I think he was part cob or even cart horse - seriously, he was enormous. But you weren't allowed to go above a trot when riding him. There is a photo of me on his back with my feet only just below the half way line on his body. You needed to be stretchy.........
This was entirely under my control, not on a lead rein - but I'd been having weekly lessons for long enough to learn all the aids and how not to fall off at walk and trot. (Canter I never really got the hang of. Hang on, yes.....)