I think in the end, what it all comes down to is how confident YOU are as a handler/rider.
I have ridden horses over the years that their owners were in awe that the horse didn't buck, bolt, spook, or pull any nonsense with on the trail. Why? Because I'm confident and work the horse in such a way that keeps his focus on me, and not his surroundings.
Too often, when a horse is focused on something scarey we, as the humans are focused on getting our horse to look at it. Forget about that aspect, and get him to pay attention to you instead; he needs to look to YOU for leadership, not look at the scarey object and keep focusing on that object. Work him around and near those things, but keep him focused on you, don't let his mind wander to the thing he wants to stop and spook at, keep his feet moving, and his mind engaged.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."