I completely agree with Ashley. It's difficult to reassure a spooked horse in the moment of him becoming frightened since his flight response will have already kicked in. The most you can do is prepare your horse beforehand by practicing desensitization exercises, doing lots of groundwork to gain his respect by moving his feet (backing, lunging, yielding the hind and forequarters, etc).
I'm going to elaborate on the idea of pressure and release and how the idea of 'release' is the horse's reward, in case you were wondering what reward Ashley was referring to.
Naturally, horses communicate through body language. When a horse wants another to move, he will approach the other and, by doing so, will apply pressure to this horse. The horse being approached will move away from this pressure and when he does move away he gains release. Horses will always learn from the release of pressure since less pressure is positive for the horse. Therefore, this horse has learned that if a horse approaches, if he moves away (the right answer) he will gain release and is able to relax. We can apply this idea in training - especially in desensitization!
There are numerous videos available on youtube which explain how to desensitize horses. Clinton Anderson is especially good at explaining this and applies the idea of pressure and release to his training methods. I highly recommend checking his videos out to benefit you and your horse!
First of all you need to know that the horse is a wild animal who survived by running away, this is why he kept this fear of basically everything. Genetic also have an impact on the personality of your horse and the way he reacts.
You need to find your horse's trust in order to make him forget his fear.
Horses have a dominant eye which sees better than the other one, this is why he will be more scary on one hand than on the other. Identify his dominant eye to know when to be more careful.
To teach him to face his fears, you can do a lot of on the ground work. Do something that scares him (for example a loud noise) while he's free, reward him if he doesn't move, make him canter if he tries to escape and stop the noise at the moment he stops running away, then reward him. Do it several times and at the end he will understand that he can trust you and running away is not a solution.
When you're riding him, give him reins to let him discover the environment (especially during walks) and don't block him otherwise he will try to run away.
I hope i could help you, good luck and don't hesitate to desensitize him, you will have a better link and trust together and can only bring good to your relation :)