Adamant1
To add to that, there's a similar thing near where I live running along the side of a church like this one is, although not on their property per say, but the church is still responsible for it. 
A bunch of kids broke glass bottles all over it and the church was the ones that cleaned it up. So they probably don't want horses on this one because of what I already said, and also because any damage to the cement they might cause with their shoes would probably be on the church or people next to the trail to repair. 