Tricky one. I was hirsute before I met Mrs P but have been clean-shaven ever since. She never asked me to, it was just an unspoken agreement and I'm happy with that. For many guys a beard appears to be a statement of that bloke's idea of what he ought to look like, not how others see him. But not always.
A curious example. One of my former managers sported a really luxuriant Groucho-style 'tache, indeed he bore a strong resemblance to Groucho if you can visualise Groucho grown to six feet tall. It was certainly an integral part of his physiognomy, and it was hard to visualise his face without it. So one Xmas, when photos were taken, some wag had the idea of photoshopping the moustache out and posted the result. Almost unrecognizable of course! When the 'victim' saw the picture, he blew his top (in a good-natured sort of way). "Don't ever even think of pulling that one on me again, anyone..."