I am really bad about not caring where my horse is looking. Sure, I just ride trails and never had formal instruction, so that's probably why.
I do have a friend who will never let her horse turn it's head anywhere but straight ahead and the reason she gives is that the horse(s) are looking to spook if you let them do that. I haven't really found that to be the case. And that they aren't paying attention to you (which I'm sure is true). I try to pay better attention on the ground, with my yearling, that he isn't sight-seeing all the time, but for the adult horses I never even think about it. As long as the horse is going in the direction I want, I don't really pay a whole lot of attention to where the head is turned.
So I must be one of those annoying people.