Horses have a life separate from what we share with them, a life of social interactions, and hierarchy amongst their own kind, and a social standing that is partially learned, and partially inherited from the dam. A horse who is terrified of other horses is often one that is low on the social scale in a herd situation, and is concerned about other horses beating it up any time they see another horse, as this is what they have experienced so far in their lives, or previously in their lives. They do not think that their human can protect them from what they know to be true… that they are going to be beat on by another horse. They have no self esteem. The other option can be that the horse is HIGH on the social scale, and normally gets all other horses to submit to them in advance of any challenge to their high social status, BUT, when a rider is on the horse or when being “controlled” by a human, they feel unable to dominate other horses as they normally would without a rider to hamper their efforts. Since they can not sort out their dominance quickly and in advance of actual interaction, they feel threatened, thinking that the other horse is going to beat on them, and they can not defend themselves or assert themselves as they would without a human involved. Thus, the spin and bolt happens from both types of horses.
It is a hard thing to change, how a horse feels about himself/herself. You are only a human, after all, and communication and understanding from a horse’s point of view is difficult, a cross species communication barrier. About all you can do is become more influential in your horse’s life, give him good directions to keep him safe, and hope to increase the trust he puts in you in situations where he would otherwise turn and run/bolt. He must come to trust your input over his own ideas/beliefs.
This is not a “bad behaviour”, it isn’t something that a horse can help, how he feels. It can definitely be a dangerous situation, for both horse and rider/handler, and it is wise to know in advance if your horse suffers from these insecurities, and act accordingly. Riding with another horse who your horse will consider to be a protector (other than you) will help, but the key is for your horse to consider YOU to be his protector, to rely on YOU to keep him safe in every situation in which he would otherwise feel afraid. Because horses are often afraid, they are prey animals. Healthy fear is what keeps them alive, they think. And running away is their prime life saving activity.
Good luck with your horse. Get her broke in an arena situation before riding out on the trail. “Broke” means responding adequately and reliably to all cues, and keeping her attention on the human when asked to do so.