You know, about horses, my big brother exercised horses at the race track for several years. I'm not sure what he did, but he certainly didn't get on them. I guess he walked them around, and I saw him play with a horse once - how's that for a visual? He sort of patted his knees like you would for a dog, then the horse did some sorta of "Ya I wanna play" and then Bro sorta made like a bear and lumbered to the horse, who cantered off and came back again. Equine tag, maybe.
Anyhow, any kind of horse establishment might be delighted to hear from a possible volunteer. Maybe you could go have a look see.
How are you with animals generally?