Bombproofing/desensitising your horse is a safety issue. You don't want to be riding along and suddenly it jumps from under you and you break a bone in the fall. And it gallops off and takes a month to find. You don't want your horse rearing suddenly and whacking you in the forehead with a hoof leaving a lump the size of a duckegg. You don't want spooky horses period.
The best time to bombproof a horse is as a foal, but if you get a new horse that has been bred and owned by other people, it is still possible to bombproof it. It takes a little time and effort, but believe me, it is worth it.
The first thing to do is find something moderately scarey, like a small paper bag. Rub it in your hands so that it makes noise to get your horse's attention. Hold it out to him so that he can see clearly what it is and let him smell it. Once he realises by sight and smell that it isn't harm full, you can place it on his shoulder and see what happens. He will probably watch what you are doing. Rub it around the shoulder for a bit so that he gets the feel of it. Then rub his belly with it and then the neck working towards the head. Then do the flank and rump. If he moves away, stop for a moment and start at a place where he didn't move. Work you way up or down, till he stands quietly for the movement. Then rub under the belly and touch the udder or gentials of a male horse with it.
I am not being "rude" here. Part of the trust you build with your horse depends on these areas being touched. It is trusting you not to hurt it.
Then rub the tail area. Then work back towards the head again and over the nose and eyes, and up to the ears. This will be trickier than anywhere else on the body, but going back and then forward till he totally accepts it is easiest for the horse and for you.
Now go onto the other side and do it all again.
Don't ask me why, but horses are two sided creatures, and just because they are calm on one side they will be spooky on the other unless you go over it again. I have seen this so many times on all horses.
Once it is okay with the bag, do it again the next day and the next till it is actually bored with you doing it.
Once your horse is happy with the little paper bag, get something a bit bigger and a bit noisier, like a supermarket plastic bag. Do the exact same thing. Make sure it makes lots of noise while you do this.
Then a large plastic feed bag, preferably a coloured one. This will be fun, because it will smell of food and be quite tantalising, but maybe harder to get up to the eyes and ears. Persevere.
Doing it until the horse is bored means that it will ignore this from now on, and bags will not be an issue with it. I also like to leave a few tied to the fences, because then they see them flapping in the breeze, lying around and learn to ignore stuff that is unusual. This also helps with shying when mounted. Flappy stuff is just not an issue.
Next you need a tarpaulin. Spread it out and place it on the ground. Lead your horse to it. Let him look at it and if necessary smell it. Sight and smell are so important to horses. Next you are going to stand on it and give a little tug on the lead. It might take a bit, but sooner or later he will put a hoof on it. Make a big fuss of this, what a good horse etc. My horses have always responded positively to verbal encouragement, so I hope yours do too. If he puts and foot on it, then backs off, try again slowly. Keep urging him on till he will put two fee, and then four feet onto it.
The main reason they are not sure about it is because it is different footing to what they are used to. You can use the same method for teaching them to walk over anything, including gravel. But remember, gravel is pointy and sharp and hurts if on it for too long.
Next, get some family members to blow up some balloons. Get a pin or a needle and go near your horse, and pop a couple. He will probably spook and run around excited. Pop a few more, and then go closer to him. Again, let him see and smell them. Pop them away from his face. but keep popping them. Keep it up till he ignores it. Then pop a few more for good measure. You might need several bags of balloons.
Now for the umbrella. A rainy day is good for this. Go out to where your horse is with the umbrella. It will make him focus right away. Talk to him, so that he knows it is you there. As you get closer and he sees it is you, he should come closer if he normally does.
Close the umbrella and do with it what you did with the paper bag. Then when he is okay with it, put it up slowly. Make sure he can see what you are doing. Hold the umbrella up and let him see and smell it. My boy took to mouthing the edge of it, so if he does this, you are getting there.
Now put it over his head. Hopefully he will put his nose up under it to smell underneath. Put it over his ears. When he realises he isn't getting wet, that is when you have him. I don't know why, but horses like to have their heads out of the rain. The umbrella will be something welcomed around your horse. Be slow and be patient.
And there you have it. Find all sorts of different things and use these methods for them. Eventually he will get so bored with your new things he will just stand there as if to say, "Now what? Is it dinner time yet?"
Lead him various places as well so that he gets used to the neighbourhood. Let the neighbourhood kids come and pat him and get him and them used to each other. If there are horse crazy kids around, encourage them to be friends with your horses. Kids seem to be fascinating for horses. They can be very calming for your mares as well.
Everything you do, do it till your horse is bored with it. But not sour. Then less things are likely to upset him, and it forms the basis for other scarey things, like trailers, vets and dogs.
Have fun with your horse but let him think he is the one having the most fun.