Yep, nip it in the butt. I have used a halter and lead to back than in a firm voice, and have also used a crop and or my body language and my own body to act rather than react, when it comes to my gypsy gelding when he was a few months old he thought he would begin by sneaking in a nip. It was quickly remedied by teaching him back back back meant get out of my space.
It is easiest if they respect or know their place on a lead away from food. Then transfer that to the food aggression situation. Sometimes they are a bit overly dramatic when training and sometimes some are more stubborn than others and take more assertive pressure to train. Honestly, when training on a lead, whether it is crowding, nipping, getting ahead of you......getting them to understand "BACK BACK BACK!" while using whatever means to achieve it (some horses only need you to yell it, stomp in their direction and pull the lead down and in towards them, others you may need to swat the ground with a whip while saying it, and others may need you to use a crop against their chest).
Trust me, you won't mame them, any of these methods are much gentler than how they treat each other other, yes, they may get wide eyed and temporarily think you are going to kill them, they key is, you only use as much pressure or force needed to achieve the result. In other words if yelling back back back and yanking the lead is enough, then that is all you use. Some horses are more stubborn about being in charge. I do not condone abuse, however, when they are seeing you as their counterpart, you must posess the role as the alpha, being in charge, a leader and being fair, using enough force to be in command without setting out to be aggressive.
You wouldn't set out running after them across the entire turnout with a whip after they have moved back several feet from your space, THAT would be aggressive. You will be surprised how groundwork/respect can correlate to situations like these. Neither of my big guys dare step up and push into their feed pans and eat prior me giving them the okay. Don't get me wrong, my mare gets huffyand sighs and, at times, if I did not turn and say back up, she would push her limits. I do not get angry at her frustration, it is her personality to stand back and huff like a pouting child, I only take discipline her if she acts on her impulse. She backs and stands, and patiently waits, even with a little mumbling under her breath, so to speak, she getsher feed.
There are times when it is human error and natural instinct that has brought on this behavior....such as putting a horse into a close group feeding situation where they feel they have to fight for their meal. This takes time to fix and change their mentality, but none the less they need to view you as being in charge.