I mean, you don’t HAVE to sell your house, obviously. But if you bought in the community relying on using the communal horse facilities, I imagine you wouldn’t be happy to have to look for boarding or facility use elsewhere. Especially if you were still paying ongoing fees. Even if you weren’t, wouldn’t those facilities have factored into the price you were willing to pay for the property? Maybe you can no longer afford your mortgage if you also have to pay board somewhere else. (I’m not saying I’d plan my finances that way, but somebody might.) Also if everyone slowly gets disgruntled with the facilities and moves their horses away, the community ceases to function the way it was intended, as others have described happening IRL.
To me it’s just not hard to see how the stakes would be higher if you’re buying a property both for itself and for some communal amenities that might not work as expected and that you’d need to pay more for / drive farther to replace if they don’t.