When roaming, domestic animals such as horses, cows and sheep (though probably the other ones too) DO NOT EVER stop, they just constantly walk round and around.
However, when leashed, they are frozen solid, and will never move unless pushed (though I don't remember is this is in vanilla as well). Why not just use the vanilla behavior instead?

https://youtu.be/OKonYjuCQCE video demonstration

mod list?

Attack Through Grass was absent when I posted the bug report