I think desensitizing should BE emotional control.
A horse's natural instinct to scary things is to run away a safe distance and then turn and face it to see what it is. The point of desensitizing should be to get the horse to realize that it can look at the thing without first running away.
The horse will run first, before thinking, because instinct says, "Run now before you are unable to run"
It WILL twitch, or jump. That cannot be helped. It's hardwired into any startle reflex. Obviously you can't desensitize to every thing they encounter. You desensitize completely to things that they wear on their bodies, like tack. And to the feel of the rider's legs, and the bit, and the noise of things around the stable.
Horses that are taught to stand there and accept scary things at a dead stand still are often just stuffing down their fear, locking up. As long as they stand still, they can endure. But the minute they start to move, the need to flee comes out and they explode. The have no emotional control because the fear is kept supressed, builds up and then comes out in a rush.
Allowing them to move forward, indeed, insisting that they are able to move forward while feeling fear, will help build emotional control . It helps becuase they have an outlet (their hindquarters), and they do not feel that they will be punished for simply moving when scared. Instead, they learn that it's ok to move, but not necessary
to all out flee possible entrapment. They learn to move a bit, then they are still mentally available to the rider, so the rider can plug in and help them deal with the scary thing. It builds a willingness to look to the rider for leadership. A horse that stuffs it down at a rigid standstill, then when you put a leg on explodes is no longer mentally available to the rider. He is emotionally GONE.
But, for new things, if you can teach the horse that scary things can be dealt with at a walk, then he is less likely to have the reaction of panic dashing.
So, if you do desensitize to tarps and thing, it's important that the horse is not just standing there accepting this becuase he HAS to, but that he feels ok to stand, OR move forward. Horse