Hi,
https://www.openstreetmap.org/way/1243313003
https://www.openstreetmap.org/way/1243313004
https://www.openstreetmap.org/way/1243313005
https://www.openstreetmap.org/way/1243313006
are no riding centres (leisure=horse_riding).

https://www.openstreetmap.org/way/1243313006 looks like a round pen (small round arena).
https://www.openstreetmap.org/way/1243313007 may also be riding arena.

riding arenas are usually tagged leisure=pitch + sport=equestrian like here (mapped by you 2 years ago): https://www.openstreetmap.org/way/1243313007

Compare
https://wiki.openstreetmap.org/wiki/How_to_map_a#Riding_centre_(equestrian)
https://www.openstreetmap.org/way/1237619664#map=17/19.41144/-99.21258&layers=P