I personally have no reason right now to leave the halter on any of our horses. They come running when they see us, so it isn't a problem to catch them. When my mare, KaZhina, had a beebee, we put a halter on him so that he would get used to it. He did fine and we only left it on for a month or two. We would never leave the rope on, as horses WILL hurt themselves on a dangling rope.
I would personally find it really irritating if I were a horse, so I guess for me it's a comfort issue. I want my horses to be comfortable. Good post!

I didn't know this forum had a horse section, that's awesome!