Under saddle, if my horse reaches for grass, she gets a firm "no" and I ask for forward motion. If I ask her to keep her feet moving, she can't graze, and she soon realizes that she doesn't get to graze while she's resting - or walking - because I'm going to ask her to move out.
Walking on a lead, I again will give a firm "no" and keep walking. If you stop every time your horse stops, you are telling him that when he wants to eat, you stop. Just keep moving, and tell him no. It might even help to jog - he'll be taken aback by the change in pace and it will shift his attention back on you. It also, again, sends the message that grazing, instead of listening to you, will only result in more work.