A couple things that have worked well for me is to first, do groundwork in a new area each time we work. I like to do groundwork a little bit before I ride, even if it's just getting them to yield their hindquarters in a circle each way, and drop their head. Something to show me they're listening. If they aren't, we do more. Sometimes I do it in the arena, sometimes in the round pen, and sometimes in the grass right outside of the pasture. That way they learn that anytime I'm around, they need to be listening. There isn't a designated work area.
If they decide to drop their heads to eat, I "pop" them with the lead rope, similarly to what tinyliny was talking about, and say "head up". Each time I anticipate them dropping their heads to eat, I'll do it again, until they can stand quietly and wait for my instruction.