This is tagged as highway=bridleway, foot=designated, and access=private, which does not make sense (i.e. it's tagged as a bridleway, but all users except pedestrians are forbidden, implying it's a footway).  If it's a permissive bridleway, it will need horse=permissive adding.  If it has been redesignated as a public bridleway, it needs bicycle and horse tags adding (and ideally access=private removed).  If it's a public footpath and not a permissive bridleway, highway=footway might be better.

https://wiki.openstreetmap.org/wiki/Tag:highway%3Dbridleway
https://wiki.openstreetmap.org/wiki/Tag:designation%3Dpublic_bridleway