To reproduce:
1. Tame a horse.
2. Put a leash on.
3. Slowly hover up.
4. The horse should be off the ground too.
Linked issues
Comments 5
Leashes snap only when you move too far or too fast. They do pull mobs. It is useful sometimes to pull them up. I don't see why it is unbelievable that such was intended
I'm pretty sure this isn't a bug.