If I was going to argue anything, I would argue for better mass transportation for horses. When I was researching before, that was the only part I could really hate, but even then, other animals are transported the same way, like cattle.
By the way, there really is no way to make a world wide ban on horse slaughter, or really anything. Just look at world politics, country's cultures, lifestyles, religions, and rules are just too different. There is no world government, regardless of how many countries or organizations think there is.
If you are really interested in stopping horse slaughter, here is the way to do it: stop the demand for it. Make people not want to eat it, not want to use it. If they stop buying horse meat, there will be no market for the horse slaughter plants, therefore they won't make a profit, therefore they will have no reason to slaughter horses.