Hi,
The tag leisure=horse_riding is not appropriate for simple riding arenas (or round pens) like
https://www.openstreetmap.org/way/1174219775
https://www.openstreetmap.org/way/1174219778
https://www.openstreetmap.org/way/1174219780
The wiki recommends to tag riding arenas leisure=pitch + sport=equestrian instead; the horse_riding tag is for the whole riding centre, see
https://wiki.openstreetmap.org/wiki/Tag:leisure%3Dhorse_riding
and
https://www.openstreetmap.org/way/1022894478

In JOSM you can find the preset for riding arenas if you search for "equestrian".