Work your way down to the ground (on a box, on a board, on the ground) so that while he interacts with you, he won’t eat food laying about unless given the release cue. Eventually you can scatter food on the ground as an increased distraction while training some other behavior.
If you increase the value of the objects in small enough increments so he can succeed, he will eventually learn that yes, he CAN ignore a field full of new grass as he walks through it unless you tell him it’s okay to help himself by verbal or dropped lead. (This, by the way, can make a great reward for a behavior such as walking calmly along a trail and periodically reward him with a minute or so of eating new grass.)
To generalize this to objects you don’t want him to mouth, grab or otherwise interact with, provide him with a sample of it and start training from step 1. Move the object out of reach/sight and reward him with a treat, not the thing he wants to grab.
Add distractions in his home training area, and train in locations of increasing distractions. These will all help to solidify and generalize the behavior in your horse.
Remember to keep all training tasks simple for your horse to be successful. Break each behavior into simple steps he can accomplish. As his trainer, it is your job to help him be successful. Avoid lumping.