Hi,
I assume that https://www.openstreetmap.org/way/1442545471 is the covered arena that can be seen on https://www.facebook.com/profile.php?id=61577859094941. If this is correct it can be tagged as leisure=pitch + sport=equestrian + covered=yes and the building/roof as https://wiki.openstreetmap.org/wiki/FR:Tag:building=roof or perhaps as https://wiki.openstreetmap.org/wiki/FR:Tag:building=riding_hall. Thcovered arena is not the equestrian centre (leisure=horse_riding), the  equestrian centre is represented by https://www.openstreetmap.org/node/13236111489, and I don't think we want to have 2 equestrian centres mapped in OSM where in reality there is only one.