Let me start by saying that I have never high-lined a horse.
But... the stable where I board the owners do it all the time. They offered to let my horse and I come out with them on some of their weekend rides this summer. They say that they usually start working with a new horse on high-lining two or three days before a trip and have never had any trouble.
Don't know if that helps or not, but they seemed confident that any horse could do it relatively easily and without much fuss.