Riding lessons are the obvious answer and, for most families, not the realistic one. There is a lot of ground between "nothing" and "a horse".
A real brush set, used properly on a toy horse, teaches the actual sequence a stable uses and gives a horse-obsessed child something to genuinely practise, rather than just hold.
Many stables offer a one-off "meet the ponies" or grooming session with no ongoing commitment. It is worth asking, specifically, whether a single visit is possible before assuming the only option is a full lesson course.
A child obsessed with horses is often more interested in the daily care — feeding, mucking out, the routine — than in riding itself. A book built around that, rather than a story, often lands better than expected.
No. Plenty of horse-obsessed children stay happily obsessed without ever riding regularly, and there is no rule that says the interest has to lead there.
A farm with any horses at all, even briefly seen over a fence, still gives a real point of reference that no toy can substitute for.
Part of our guide to Gifts for one obsession.