Does it serve a ceremonial or symbolic purpose? Is it even a mustache? I'm talking about the bushy dealio, typified in this picture.
The Mempo function is primarily symbolic and has the practical effect to scare the enemy. It often represent protective spirits, ancestors or demons and folkloric malevolent creatures.
If the ancestor, spirit (Shoki, The demon queller) or creature (the japanese equivalent of a goblin for example) has a mustache in traditional depictions, the mempo will be decorated accordingly.
The menpo, more often fashioned into a rather gruesome smile that literally emanates power, often having exaggerated features (most commonly recognised though are the mustaches and beards, though you'll see just as many with fangs of tigers for example, and quite often broad noses) - a mask designed to give the samurai a fearsome look, though funnily enough was never really used in battle. It was quickly decided that this mask, whilst intimidating, restricted breathing and field of view (being unable to see down to your feet, for example), and so was abandoned when you actually took to the fight. Most often lacquered red to give an even more intimidating and aggressive feel (as if there wasn't enough already), you could imagine how terrible it would turn out if the person you have come to greet saw you in an intimidation mask. They were often shaped to match the evil spirits that permeated throughout Japanese culture, in various forms, but essentially they represented evil, death, and so on. As for the mustache, they were most often formed out of horse hairs.
The face guard is often a depiction. It's an art form in itself as some of the casts are remarkably detailed and imaginative. This notable work is on display in New York City's Metropolitan Museum and serves as a unique example. This was a non-combat work, serving more as a decorative heirloom, but combat armor was also decorated. A mustache, though common, was not a necessity nor does it have any particular importance attached to it itself. It's just a frequent part of whatever happened to be depicted.