I know a horse who is terrified of thunderstorms. I know another horse who will completely ignore them as long as you don't actually ask her to go out in the rain - and she'd probably do that too, except I wouldn't be that mean.
Why are some horses afraid of a stimulus and others not? And what determines what each horse is afraid of?
Basic personality does enter into it. Some horses scare more easily than others, and some horses are actually anxious in the true sense. However, it's more often a result of training. A horse can be trained to not be afraid of specific things - a process called "bombproofing" - and the trainer will generally focus on things likely to be an issue in that particular horse's life. For example, a show horse might be taught to ignore applause (although some show horses will prance - they know it's for them, trust me), whilst it's more important for a trail horse not to be scared of passing trucks.
Sometimes horses may have had some kind of bad experience that makes them scared of an object, a situation, even a color. A horse that's afraid of dogs may well have been chased by one. And occasionally a horse seems to have a genuine phobia - something they've never encountered before eliciting not just a spook but absolute terror. I've heard of horses being randomly afraid of cows, pigs, and even miniature horses - like, really? It's another horse, just small...
So, it's about the animal's personality and it's past and training.