Hi,
I think the tag leisure=horse_riding is not appropriate for areas like https://www.openstreetmap.org/way/1254401965. I think these areas can better be tagged leisure=pitch + sport=equestrian (example https://www.openstreetmap.org/way/1176023068). iD has a preset for this tag combination with name "Horseback Riding / Rodeo Arena". And isn't it similar to a rodeo arena?