OK, I know I'm probably about to be shot down in flames for allowing my horse to do this but, hey, it's a forum, we're here to share . . .
My 6 year old Samson has this habit of gently nuzzling me until he has a piece of material between his lips (a sleeve, a jacket hem, etc). Sometimes it's in his teeth, sometimes not (and here I shall emphasize gently as I can easily pull away from his grasp, he isn't clamped on for dear life). Then he will sigh, his ears droop, his eye glaze over and zzzzzz . . . He would stand for hours like this sound asleep, with me attached, if I let him.
In 40+ years of horses I've never had one do this before and I find it kind of endearing. It puts me in mind of a child taking comfort from his security blanket, only I'm "blankie".
*steps away from screen to don flak jacket and helmet*