Hi,
https://www.openstreetmap.org/way/1147258471 looks more like a riding arena to me (pitch + equestrian).
https://www.openstreetmap.org/way/1147258472 and 
https://www.openstreetmap.org/way/1147258473 : I don't know, large enough for riding arenas, but look more like paddocks on bing.
https://www.openstreetmap.org/way/1147258484 and
https://www.openstreetmap.org/way/1147258485 they can't be riding arenas, let alone riding centers.
The tag leisure=horse_ridng should be used for the entire riding center and not on individual parts of it, remember
https://github.com/openstreetmap/id-tagging-schema/issues/413
Maybe there is something wrong with the translations (?)