I'm having several ideas regarding beards and hair.
1. Beard and hair should grow over time.
2. Female characters should be able to grow a beard.
3. There should be barber profession to keep your hair and beard stylish and tidy.
4. If you don't maintain your hair and beard there should be penalties.
* 4.1 You should trip over the long beard.
* 4.2 You should be blinded by unattended hair.
* 4.3 NPCs should dislike bear looking characters.
In response to your 1-4
1.) I agree that facial hair and head hair should grow over time. It adds another aspect of the game that would be pretty cool. Besides if you want a "viking" like character, why not let it all flow out? This is a good idea and the only way it should be able to be cut is by reporting to a town barber. (Unless you do it yourself)
2.) WHAT?........... umm, how about NO! My main character is a female and I absolutely do not want her growing a beard. Women are supposed to have soft, pretty faces. Not gruff, beastly looking ones. Also, how many woman in real life do you know that have beards? Women do not grow full fledged beards. Maybe a little bit of very fine hairs on the upper lip and cheeks, but not a beard (unless they are taking testosterone pills).
3.) I agree. The barber profession would be great. That could be another added in-game profession if it were implemented. I also think that you should be able to change your hairstyle at any given time (at the barber) during the course of the game.
4.1) No tripping over the long beard. I am all for realism, but that adds a dimension that doesn't need to be added. Not much more to say about that.
4.2) I actually kind of like this one. While your in the first person mode, if there is hair covering either eye (or both), it should obstruct your sight. If this were implemented however, it would have to have an option to shut it off.
4.3) Just like in real-life, people have opinions of other peoples hair styles. They can actually say a lot about a person. I agree with you on this one.