I saw someone draw Link with a beard, and I did cry. It's just not meant to be that way!
Though what I would go for is a design-your-own-Link. It's not the kind of feature Nintendo likes to offer, but I think the reason Link is kind of androgynous is partially because Nintendo wants him to be able to "stand" for any player, including female players. As opposed to Solid Snake or the dude from God of War, who are both extremely masculine. Then again, I might be reading too much into it. Yeah, probably.
(Edit: Nice beards, guys!)