Hi,
I think, for a rodeo arena the tagging leisure=pitch + sport=equestrian would be more appropeiate. Example
https://www.openstreetmap.org/way/702162073; the iD editir recognizes this area as "Horseback Riding / Rodeo Arena". In JOSM you can use the preset for "Equestrian Sport" to set these tags. See also https://wiki.openstreetmap.org/wiki/Tag:leisure%3Dhorse_riding