Three things come to mind.
Animals familiarize with things through sight, smell, hearing, touch and taste. Generally taste rules over touch, for obvious reasons. Horses are common to lick chew and taste things for familiarity. We touch things with our hands more so then tasting things, a horse is the opposite for the lack of arms. When an owner is really puzzled over a horse mouthing things, I don't think they realize the concept that horses are very orally prone. It's of course good to analyze a horse's diet to see if a mineral or vitamin is insufficient, but it may very well be just a mouthy horse.
With that said, when a horse eats hay they continue to chew until there is no longer any more food in the mouth. They keep feeding the hay through their mouth until they choose to move on or the supply runs out. The horse may just be naturally feeding things through his mouth by habitual eating, causing him to seem as if he's wanting to eat the entire lead.
And third, like said, this sounds like a case of boredom. Don't be so surprised how quickly horse's learn one another's habits. After all, they are very observant due to their natural instincts and a bad habit may be being passed around the barn like a case of the flu.
If it bothers you, I also recommend the vinegar/lemon trick.