In order to fix the problem with the ghosting horse armour, I had to restart the Launcher.
After coming back into my world, the ghosting horse armour was gone, but all of the leashes went invisible, although the animals were still attached with them to a Fence.
In order to make them visible again I had to unleash them and re-leash.
I will attach Screenshots.
Edit: Here is a short video where you can see it (no audio):