What have you set the attachment points for the cables? I’d assume you have two cables, one for each hand connecting from the hand to a socket located on the horse bridle near the mouth.
You can enable collision on the cable in the cable settings, but I’m sure the collision is spotty at best with it… (if it works at all).
There are assets in the marketplace (linked below) that I’ve used that have done this really well, where the bridle is a skeletal mesh and animated appropriately with the horse’s movement.