A bombproof horse is the opposite of a spooky one. The term comes from military training and cavalry horses being taught not to spook at explosions.
True bombproof horses are very rare (I've only known a couple). Any horse will spook given enough provocation, even old reliable pony ride ponies.
"Bombproofing" is another term for desensitization training - these days it's mostly done by show people and also by mounted police, and involves exposing the horse to all kinds of scary things in a controlled environment until it settles down and realizes they aren't so scary.