On most horses on (2 hour ish) rides if we have to pause for a second, they better not dive for the grass. If we have to stand still for a few minutes grazing in one spot is ok, but no wandering around. And if we're walking, if they can snatch a bite ever once in a while without disturbing their walking, it's fine, but no stopping or slowing or turning around just to get that mouthful of leaves.
On Velvet though, if I let her get the tiniest mouthful of anything that's all she can think about for the rest of the ride. She's just four though, I doubt she'll always be like that.