Honestly the youtube videos are only showing the worst of it.
I'm neither pro nor anti slaughter...I'm somewhere in between. I don't like that it's a necessary evil, but that's just what it is. If there was a legitimately humane way to do it, I'd be all for it. Alas, there is not. I've never heard of the electrocution method. I do know that the bolt gun more often than not does not kill the horse and many horses under the bolt gun method are actually conscious when tied up to be slit...which I do believe to be illegal. I like the one place in Canada where they just put a bullet into their head...
In my perfect world (with slaughter still necessary):
It would be illegal to slaughter companion horses for consumption.
Private owners, kill buyers, etc. would not be paid for providing the animals.
Euthanasia for companion horses would be extremely affordable/readily available.
Food horses would be raised for such, like cattle or other consumed animals.
But so much for anything being easy.