Warmth: Since prehistoric gender roles were probably as silly as ours, (cave)men probably engaged in manliness contests similar to the displays of mountain gorillas. If these contests consisted of staying outside in the cold for as long as possible, the bearded male would have had the edge and produced more children due to not being dead. Women don't have beards because they were too busy being inside cooking dinner and gossiping. Unfortunately this is not a very plausible reason as people from hot countries also have beards.
Protection: The coarseness of the hair protects the chin and neck from attack by ferrets. But ferrets also have a tendency to get tangled in beards and aren't very attractive. This is an unlikely reason.
Attack: The scouring nature of the beard makes it an excellent weapon for leaving tiny scratches on the faces of your rivals. In the harsh and unhygenic conditions of the prehistoric era, these would have become infected, leading to an unattractive puffy face and maybe death. On the other hand, sabretooth tigers have even coarser and tougher hair to protect their faces, and their sabreteeth are not going to be blocked by a bit of fuzz. We're definitely getting somewhere now.
Attractiveness:
In favor:
Against:
Usefulness: Beards have many uses, from scouring pad to exfoliator. Prehistoric women would have preferred mates who could help clean their pots and remove dead skin cells from their legs. Men with beards would also have been able to help more with their children, as they could store them in their beards and have both hands free. Women do not have beards because men would leave their dead cells on for protection, and women have more flexible toes so do not need free hands. This is unlikely as the previous sentence was really too silly as you can't stir a pot of mammoth stew with your toes, so women should have beards too.
Food storage: Beards provide a space to store the scraps of food that fall down when you're destroying your mammoth steak with the vengeance of 12 suns. The males who had extra sustenance were healthier and thus more reproductively sucessful. Women are dainty and do not drop any food, and anyhow need only 2000 calories a day. This is the most likely reason for beards to have evolved.
It occurs to me that I could have googled this. And the results are.......
Well just look at his face, he's clearly biased.