Well this one is fun… I’m going to separate from the herd mentality here and suggest a two-stage filter design. With ten horses and a dedicated pool, I am going to assume that you are an expert in “how to turn a big fortune into a little fortune”, and will adjust my design suggestions appropriately. (For those outside the loop, this is a horse ownership joke. I’ll have one too when I get to be a big boy).
I am not a reigning expert around here on swimming pools. With that having been said, what you have here in my mind is really more of a hybrid between a swimming pool and an aquatic pond. You want it clean like a pool, but it’s got much more load in terms of dirt and biologic than the standard swimming pool that is usually talked about here. This is all about you, since the horses don’t give a d***.
When I was in college, I spent my summers working at a waterpark (Schlitterbahn, thank you for asking). There we ran commercial pool protocols, and while I was a diver and really did little with the pool side, my direct boss was radio codename “Pool Boy”, and I learned a great deal from him. We had this aquatic fish pond over a 400’ boardwalk deck leading to a restaurant that never seemed particularly well thought out to me.
I somehow got dragged into filter maintenance one summer. We had three 500 gallon filters on that system that kept getting plugged up quickly, and we had to drag them out and empty the sand and gravel so we could swap in some larger filter media. Putting larger media in effectively created a pre-filter that caught the big gunk and thus “saved” the finer filters for the smaller stuff. We got the job done. (Fun side note: when I got out of college [construction science] I couldn’t get a job so I came home and found one as a PM for that same company while they were building a new waterpark. Hit me up if you need to know how to build a wave pool or lazy river.)
All this is to say if I were you, I would be thinking about putting in two filters instead of one. Stage 2 is your standard sand filter mentioned by everyone else here. Stage 1 is the “pre-filter”, in which I would run something like pea gravel, or a mixture of pea gravel and something larger than sand but smaller than pea gravel to fill the gap. (If memory serves two media will fluidize and settle appropriately when you backwash the filter. I think we ran sand and gravel together as an example). I’m thinking of decomposed granite type consistency, but I don’t know if that would contribute to water chemistry and I’m sure there’s a defined product to use.
Those are my thoughts… worth what you paid from them.