The mask—and, in particular, the horned mask—is generally reckoned among the mysteries of the Horned Lord; his priest wears it to personify Him in ritual. As such, it is also accounted a men's mystery.
Why?
As is usual with the archaic, ones looks for origins to humanity's perennial preoccupation, the getting of food.
As such, the mask originated as a strategy of the hunt.
To disguise your scent and outline, you wear the head and hide of (for example) a deer. Here we see the origins of disguise generally.
It is also the origin of the personifying priesthood: pretending, in effect, to be who you are not. Disguise yourself as a deer and act like a deer, and it gives you a better chance of taking the deer that you need to feed both you and your People.
This also explains the Mask's specific (though, of course, not exclusive) association with men. Although among people who live by hunting-gathering, virtually everyone—regardless of age or sex—hunts as well as gathers, hunting is generally accounted part of the men's sphere, since hunting large animals is dangerous and (to be quite frank), in the larger life of any given society, men are more readily expendable than women.
To this day, the priest of the Horned still wears the god's horned mask at the Sabbat, and a sacred connection to our food-sources lies at the very heart of the Sabbat and everything that we do there.