Hi,
You have tagged all the riding arenas leisure=horse_riding, but according to the wiki riding arenas should be tagged leisure=pitch + sport=equestrian, see https://wiki.openstreetmap.org/wiki/Tag:leisure%3Dhorse_riding
May I ask you to retag them? In iD there is a preset for riding arenas with name "Horseback Riding / Rodeo Arena" which sets these tags.
You can additionally map the whole horse park as an area or a node and add leisure=horse_riding + website=https://www.bigskyhorsepark.org etc., like https://www.openstreetmap.org/way/422891667