Hi,
This object seems to be a building, but the building=* tag is missing (therefore it is not rendered as a building). Maybe it is a https://wiki.openstreetmap.org/wiki/Tag:building=riding_hall or a https://wiki.openstreetmap.org/wiki/Tag:building=stable
For the whole riding centre I would add a separate node or area object with leisure=horse_riding, name=... , compare
https://wiki.openstreetmap.org/wiki/Tag:leisure%3Dhorse_riding and https://www.openstreetmap.org/way/847492340