Someone who's bearded has a beard. If your grandfather is often mistaken for Santa Claus because of his bushy white beard, you can describe him as bearded.
Men with beards — whether they're trimmed short or worn long and full — are bearded. Women can be bearded as well, though it's less common, and so can Billy goats, with their tufted little beards. The adjective bearded is sometimes even used to describe plants, like the bearded iris, which grows a prominent bushy "beard" on its lower petals. Bearded comes from the noun beard, with its Germanic root, barthaz.