It really helps if you know what their previous experience has been but quite often simply retraining them can cure the problem. I have found that a lot of horses that are 'trained' to drive quite often have some huge holes in their training and simply taking a step (or two or three) back and starting over can resolve their fears.
I am so excited'to hear about everyone's interest in 'agility' with horses! I am working on becoming accredited in horse agility with the intention of starting an agility circuit here in Ontario. There is an international halter agility club/organization and I would like to follow their format adding in driven agility. I am very excited about it as it is something I really enjoy. And they do have a liberty agility class!