My horse tries this on a semi-regular basis. To deal with it, I lead him in a rope halter (that's what I use anyway, not just for this), and I pay close attention to where he's carrying his head. I realized that my boy will dip his head a couple of times, and if I do nothing, he takes advantage and sheers off to eat grass, and will try to drag me along. So I hold the lead rope fairly close to the halter (maybe 1 foot, 1.5 foot from the attachment point to the halter) and if he dips his head, I give it a little pop up to let him know I'm paying attention. At this point, that's usually all I have to do. But on the way to getting to where this is all I have to do, he'd be persistent and eventually try to yank his head down. I don't like to get in a yanking contest with him, so I keep the *other* end of the lead rope (the end with the leather popper on it) nice and loose, and if he dips his head again, I just keep walking and shoot that leather end of the lead rope out behind me to pop him on the butt. Not hard, just *there*. On the other hand, if he yanks me, he gets a good solid pop on the butt with the lead rope, and once I have his attention, he has to do some backing up and small circles. It's got to be totally consistent. Now we're to the point where he knows that I will hand graze him but only in certain areas, and I give him a signal that it's time to hand graze.
He still tries once in a while, but as I said, the way that usually plays out is he dips his head, I pop the halter up lightly, and that's the end of it.
I should also say that my boy is Mister Pushy, and his former owner had him in a chain shank, but that I haven't had to use any such thing. Regular groundwork, firm boundaries, and consistent reinforcement of those boundaries is key with my guy.