I've never heard of clicker-training a horse (thought that was just dogs, hehe) but the title made me remember a guy from one of my old barns. He had the COOLEST horse ever, who knew how to fetch! He would be loose in the arena, and the guy would throw his halter away from him and the horse would pick it up and bring it back. He could throw the leadrope, a ball, whatever as long as the horse was able to pick it up with his mouth. I always made him show me it again whenever I was at the barn.
So it IS doable! Good luck, and be sure to post a video of it when you're done!
Take a ride across the badlands
Feel that freedom on your face - Breathe in all that open space
You'll understand why God made -Those fly over states