The track to the north https://www.openstreetmap.org/way/82023921 is tagged as a public bridleway and there is a physical sign at its north end confirming this.

The two tracks to the south https://www.openstreetmap.org/way/1164672599 and https://www.openstreetmap.org/way/1164672602 are both tagged as public footpaths, which seems implausible as this would prevent horse riders from going any further.

Resurveying this area would help understand whether the bridleway continues along one or both tracks to the south.