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.
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The horse went into the water, resulting in the skeleton dismounting. Duplicate of MC-72440.

I am not sure that I agree with linking this to the other bug report (MC-72440). Only one of the four horses entered the water hole, and that was only after we engaged in combat. Furthermore, it doesn't explain the clearly glitchy behavior of the riders and horses (acting as though they are still mounted, although more than 10 blocks from each other).
I can reproduce the riders dismounting in deep water, that's easy. But they act normal (i.e. operate independently) when they dismount in that scenario. This bug is more about the behavior of the mobs: they appear to be dismounted, but they are not. The attacks originate from the horse, not the skeleton rider. You'll also notice in one of the screenshots the skeleton rider is floating above the ground.

I think you mean MC-96954 then

Yes, that is it. I was able to duplicate the scenario in that Bug Report using the Skeleton Trap.

in my creative world, i had a skeleton trap spawn next to me. I decided to yolo it in survival and tried taking it on with only iron gear... I got recked. So I respawned and flew back over to the trap to find that one the horsemen was mysteriously hovering in the air as if it had no AI but they still looked around. I assumed that this was a glitch and that the skeletons had actually dismounted their horses. I geared up again, with enchanted diamond armor this time, and got blitzed by a invisible rider as all of the other horses were moving wildly in what were effectively circles. I killed the horse and the rider suddenly pops into existence, and I quickly killed him too. I took one of the horses because I thought that the fight was over since the floating dismounted rider could not be hit. I come back to find a second horseless rider chilling at one of the nearby villager huts and I can't get on another horse sitting on the battlefield. I fire an arrow above it and the first horseless rider gets hit. I then tried my best to document it in the screenshots I will attach. It was definitely the strangest hostile mob encounter I have ever had.

just realized this was marked as duplicate, will move all my stuff over to proper thread