Parenting won't have any effect on cloth simulation (other than to get the 'cloth' item into the right place to begin with).

Vertices added to the constrained group will try to follow the surface of the nearest figure as it moves. So if you constrain some vertices at the horse end of the rope, they will follow the horse.

Vertices added to the choreographed group will try to stay where they're put; in this case, if you choreograph vertices at the wall end and don't move them, they'll stay in place during the simulation. I'm assuming the wall isn't going to move, but the horse might. ;)

The alternative, as dadt suggests, is to make the wall a figure (if it isn't one already) and constrain that end too. But if it's a prop it seems easier to constrain the horse end and choreograph the wall end.