Now that we know why horses generally respond the way they do, we can talk about what the initial introduction to horses or back to horses.
Whenever a person who fears horses comes back into contact with them, it is imperative that the horse they meet with be dead on its feet. You don't want a rhino-on-crack Arabian prancing up to them and scaring them before they even touch it.
Once a horse is found who meets these requirements, the introduction can proceed. The person will need to remain calm and in control. If the horse whinnies and they scream, it's likely that even a broke horse could spook. They need to be aware that the horse won't harm them. They can walk away at any point. Nobody is forcing them to do it.
Initially, the person should only proceed with what they are comfortable with. Feeding a carrot. Petting the nose. Stroking the neck. Remember, this is only the beginning. Someone who fears horses on the ground should not get on.
Same with horses whenever they are being trained. If you can't put a rope around their girth while you're on the ground, the last thing you want to do it throw a saddle on and go for a ride. It will be a rodeo. It's that simple.