From personal experience I can testify that Dogs, cats, kids, adults and yes horses have all been zapped on our fencing.....
I have been zapped wearing rubber soled shoes!
I had the same problem other than running the wire inside...we have ours outside using extension cords... Yeah.. I know... not the best but it works.
Anywho... I have 2 lines run for the "hot" wire. The hot wires have to be connected to each other and not touching anything else. The first line runs from the terminal to the handle for the gate which is a hook with an insulated handle that connects to a porcaline(sp?) wire holder thingy. ( I found the porcaline thing in the old barn.. its an old wire holer for electrical poles and has a screw out the bottom of it ) The second wire runs from the 1st fence post with a plastic holder to the last post before the gate and then I have a wire to "jump" the 2 hots together.
The ground is only a ground... not touching anything but the ground pole and the terminal.
Hope this helps...Good luck!