Upon further research, please mark this resolved.
Can't seem to recreate the bug, please close. If I ever learn how to recreate the problem/find the cause, I'll be sure to report with images. Sorry about that.
Not a dupe, the other one involved the lead being broken. In this one the lead is still attached. The horse (or other mobs attached) also did not die, simply took fall damage no matter how sensitively you dropped them.
I have found that adjusting the anisotropic filtering seems to fix this problem.