A horse that is very well trained and calm, that isn't easily
spooked. Term originated for Military horses who must be "
bomb-proof" so they don't
spook at the sound of a bomb/gun/etc.
Children's riding ponies often must be bomb-proof because kids tend to run and jump and make loud noises--all things that might scare an ordinary horse and cause him to hurt somebody.
My old mare
Goldie was a
bomb-proof horse-- We could drive the tractor right past her and she wouldn't even
flinch!