text: It's entirely possible to walk down the street and see that there are no signs prohibiting horses here, and there is no reason why this particular alley should be tagged any differently than any other public street..
  
  However, on the question of whether it's legal to ride a horse here, the answer it too complicated for the tagging used in osm.  Basically it is illegal to ride or lead a horse down the street everywhere in the city, unless you're riding to or from the beach or a parade (which is actually super vague if you think about it). If the horse is attached to a cart or buggy or whatever it can go anywhere (even down here, whether it wants to or not!), as long as it has a license.