Bah, I made a huge post about the evolution of beards in humans and their cultural history and so on and accidently on purpose closed the window! (My boss walked in)
So now it is gone.
I will summarize:
Beards are a classic sign of strength and virility. This is cross-culture; every primitive culture, pretty much, had the same belief, which is a sign that we are evolutionarily geared to see things that way. Of course, humans are sexually dimorphic, since we tend to have semi-pair bonds and a naturally promiscuis nature, normally in a male dominated situation - and what with beards being linked to testosterone, women generally dont get them. In fact, being linked to testosterone is probably what made them associated with attractiveness - There is an actual correlation between strong agressive males and large healthy beards. Since males historically competed over females, rather than vice versa, beards were selected for in males and not in females (females want to appear not to be a challenge). Actually, though, humans are pretty complicated - in addition to our balance of harem relationships and semi-pair-bonds, we also have promiscuis females who bank on fathers taking care of social offspring. Its complicated, but the important thing to keep in mind is that its not even, either in the goal or approach.
Now, men have more beards because testosterone causes beards, but nothing says it has to be this way - Hyena females are the dominant creatures in hyena culture, and have their own special female testosterone to give them special characteristics. So clearly the social aspect is important.
Dwarven culture is clearly different from both situations - they dont do harems, they don't sleep around, they do permanent pair bonding. Most species with permanent pair bonds are remarkably difficult to distinguish between the male and the female. In addition, they seem to be a society where males and females fill the same social and professional roles, further reducing dimorphism (though in the case of beards, the sexual inequality is really the only one that matters). So unless dwarven mating procedure is drastically overhauled, there should be little sexual dimorphism between the specias.
In addition
So, It cam pretty much be assumed that the dwarfs emerged from the colder climes much like their Norse spiritual sires, for insulation (though desert living is possible for the same reason), which can also be attested to by a dwarfs thick frame (which doesn't bode so well for the desert dwelling theory).
seems to be a pretty good summary of their likely origins, but it must be mentioned if they are naturally inclined to mountaintop areas, the cold northern climes aren't required - mountains themselves get pretty cold.
Anyways, this is a lot less in depth than i wanted, but im just not really up for rewriting the whole thing.
Final note, if you want to blame someone for the lack of beards seen today, blame Alexander of Macedonia. He decided to shave the military to increase uniformity (and rob enemies of handhelds). When he marched around, that meant the most impressive people physically tended to be beardless, which sent a lot of cultural messages. Rome decided the style was hot and did the same with its soldiers (and its upper class) because they style all their good ideas from other people. Plus being bearded was a greek thing at the time, and they were trying to assert how totally not a copy of Greece they were.