Yes.  It is fairly typical in OpenStreetMap to see roads and trails composed of multiple ways with different tags.  In this case the western section is tagged to allow horses and the eastern section is not.

Optionally, we can add a route relation joining the multiple ways into a single entity for the entire trail.  I've just done that for Talon.  Does this look like the entire path you were expecting to see?

https://www.openstreetmap.org/relation/20618001