1b. The horse dies falling off rocks ALL THE TIME.
Just be thankful it isn't the rocks falling. Then everyone dies.
But yes, the horses in Skyrim definitly need some TLC.
Personally I hold up Mount & Blade's horses, though it is a very different game. If a horse is injured or fighting something scary it should run unless you keep it there (unless, maybe, there is horse riding skills and at higher levels not only does the speed and control it also increase its desire to stay with you and protect you, unless you order it away). If it does run there should be an easy recall function.
Red Dead whistle like suggested, or whip out an ocarina - anything.