Hi, you're right about the horse riding arena. But about the relation I don't know. 
This place it's a mix of things that I found difficult to espress with iD presets.

"Cavallino Azzurro" it's an educational farm where they practice agritourism and hippotherapy.
It's in part similar to "Due Ponti Village" https://www.openstreetmap.org/way/1375830220#map=17/44.153956/12.406633

So I don't think it's correct to map the place with a relation leisure=horse_riding. 

I have a doubt about https://www.openstreetmap.org/way/1436119280: a horse-walking area delimited by a wooden fence also used as a parking lot for cars. I mapped the lot with tourism=trail_riding_station. Is this okay?
