Hi Elaine. Sorry to have taken so long but I’ve had big problems with my PC. Bill Gates has a lot to answer for!!!

Horses and dogs. You obviously know your stuff so this is more for other people who may read this. Trying to train out a behavioral problem such as this poses two major problems. One is not rewarding the bad conduct and the second is not siding with the dog against the horse!
Obviously no one would do either of these things deliberately but if you think about the first of these, it happens every time the horse passes! The horse approaches and the dog barks. The horse gets level with the dog, passes by then goes away from the dog. In the dog’s mind he has won! He has driven the horse away! He has his reward!!
In the second case, siding with the dog. The dog barks and the owner tells the dog off. Unfortunately the dog is not paying attention to the owner. All the dog knows is that both he and his owner are barking, in other words, in his eyes both are trying to drive the horse off!
I think you are right about desensitising but you cannot do that on your own. You just cannot take the risk of spooking a horse and have it maybe throw the rider. What you need is the co-operation of someone with a bomb proof horse. Maybe a riding school horse or better still, if you can find it, a helpful hunt stable. These horses are so use to having dogs running around them that they would not be too concerned. If all else fails you could go to a Game fair. Dogs are welcome there and there is usually a hunt giving a display so you have the chance to get your dog reasonably close to the horses once they have left the ring. The local gymkhana is another place to find horses although in this case the horses may well not be so bomb proof and you would need to work from a greater distance.
I would be inclined to play with my dog, gradually getting closer to the horses but at the same time, not appearing to the dog to be in any way interested in the horse. Take it easy and don’t try to get too close all at once. It may well take several trips out to do the trick. Start each session from well away and gradually move closer trying to always stay outside the critical distance. Take some time to find your dog’s turn on. Some love to play and will ignore everything except the game, some are good under orders and a sit stay works for them, with others its food. As I said at the start, be careful not to reward the crime. The play/food only happens if the dog is behaving and if it is not then it should be the dog who gives way to the horse not the other way round, walk the dog away from the horse before the horse starts to move away from the dog. This is a situation where I would discipline the dog. I don’t believe the voice should be used on its own because of the dog interpreting it as me supporting the dog against the horse so I would hold it with a hand each side of the neck and, lifting the front paws off the ground, hold eye contact while I’m telling him off. I stress the eye contact because I want the dog to be in no doubt that it is him I’m dissatisfied with, not the horse! I know the theories about not looking into the eyes because it is issuing a challenge but the leader is the leader and to me it is the dog who should look away when I challenge him, not me.
You don’t say what breed he is but in my experience I would guess BC/WS, I’ve seen several who exhibit similar traits. My guess in most cases it is part of the herding instinct coming out.
This is just a few ideas on how I would go about it. Really it is a matter of trying something and being ready to modify your tactics in a light of the response.
Hope this helps a little. Please keep in touch about it.
Best wishes, John