In theory I would love this but in practice I’m aware of a few different similar type projects and none of them lasted over the long haul.
The biggest problem comes down to the fact that you don’t just have to create the critical mass of horsey homeowners, but keep it. As people move away, or their horsey family member ages out of horses, it’s hard to keep everyone focused on the facility with the right mix of enthusiastic owners. They have to be the same discipline too, and what happens when they decide to move on to a new trainer? New people buy in who don’t have horses, and they tear out the horse facilities that are on their property, which also makes it less horsey going forward. How do you keep space for the people who own in the HOA but also keep it full enough to be a viable operation?
So I think if you’re interested in doing this, what I’d do is hunt down all of the ones you can find, and then I’d learn from the case studies, which ones have worked and which have not. Also look at barns and horse parks that are tightly connected to residential areas but not sharing an ownership interest and see how those have worked out.