This was the scenario:
A Skeleton Trap was activated. I made a tactical retreat to the other side of my house to attack the mob from the opposite side.
When I found the four horsemen again, they all appeared to be dismounted from their horses. However, I could approach the skeletons and would not be attacked and I could not shoot them. Instead, if i approached the riderless horses, I would be attacked by the horse with arrows (as if there was a rider on it).
If I killed a skeleton horse, the skeleton rider would appear to teleport to the location of the dead horse and then would attack if approached or in range.
I even killed one skeleton by shooting just above the horse (where the rider would be), all while the skeleton rider was standing next to me. Once the rider died next to me, the horse stopped shooting arrows (see the screenshot with the skeleton next to me and the horse in the water hole).

Included the four screenshots that I could make during the heat of battle.
Also, one screenshot showing the Debug screen, if that is of any use.