I saw that a few people have recommended getting off and walking your horse, in situations where he's spooky.
I'd strongly recommend AGAINST doing this, in almost all circumstances. As much as it might not feel like it, you're usually safer on your horse, in those types of situations. If your seat isn't good enough to be able to stay in the saddle while your horse gets a little spooky, then you probably shouldn't be riding out alone. You don't want to be on the ground, leading your horse, if they're acting a fool, you're likely to get hurt...
I could not disagree more.
If I can choose to be on the ground or on the horse when the horse hits the fan, I'll choose the ground every time. Worst case, which has never happened to me on many walks, I can let go of the lead. If my horse then bolts into traffic, she would die and I would not die with her.
Here in southern AZ, a bolting horse can take you thru cactus or into a hidden wash. One about 50 yards from my house is 10 feet deep and hidden by vegetation until you are within a few feet of it. A bolting horse would kill herself and her rider if she went that way.
But it has never happened. It is much easier to control a nervous horse from the ground than from in the saddle. They are much less nervous once they see you, for one thing. Nor has my mare EVER tried to go over me. When she can see me, she knows where I am.
I think the key is to learn your horse well enough to know when the scary thing is getting nearer, rather than wait until your horses legs are spread out and her eyes rolling. At that point, you have lost. Even if you get the horse to 'go', it becomes such a big emotional event that my horse, at least, has just learned that it is REALLY scary.
When she is startled, she hops sideways and then stares. Those can usually be overcome with a bit of time & talk until she approaches what startled her. But if she genuinely is afraid of something ahead, there are warning signs. Learning those signs, and getting her to go far enough to be uncomfortable but not so far that she squirts liquid poop out the rear is "success".
Success doesn't mean 'make her go past the culvert'. It may mean get her closer to the culvert today than yesterday, and closer still tomorrow. It can mean 'lead her past it on the ground today', followed by lead her up to it tomorrow, and let her stand next to it for 10 minutes after that, and then ride her past it.
I don't think horses are acting scared. When my mare rolls her eyes and squirts poop, it is a real fear to her. Desensitizing is a matter of pushing the envelope, not exceeding it. Push her until she is nervous, but not until she freaks. The first teaches her you are a good leader, the second teaches her you are cruel.