I'm not sure about wild horses, but I have spent some time observing moose, which seem like a similar design. They don't seem to have much of a sense of purpose

I'm not sure about wild horses, but I have spent some time observing moose, which seem like a similar design. They don't seem to have much of a sense of purpose. So once scared into running, I don't think they would run very far before stopping to browse on some berries or nice grass.