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!
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