I'm no expert, R&R. I just have known some people into horses over the years and I know nothing at all about local riding opportunities, as I don't ride.
When I was a kid, living for a few years in the chicago area, we could, as children, go to the local forest preserve and sign up for a horse for an hour.
This was a long time ago.
I think ehBeth is probably right, that facilities are very wary by now about insurance matters.