Because this isn't real evolutionary biology and no peers are going to be evaluating my work, I'll feel free to propose the following just-so story about dwarven beards.
First thing you need to know is the dwarven mating system is rather unlike the human one. Dwarves are strictly monogamous and females mate only in the context of a long-term committed relationship, i.e. marriage. Why THIS is, you can invent all kinds of other stories about. The upshot of this is that while females do have the larger zygote and carry the baby, both sexes have about equal parental investment in the baby, since males stick around and contribute as much as they're able to the marriage and child. This leads to very little sexual dimorphism, which is why male and female dwarves are pretty much identical in behavior and physiology. Therefore what's good for the male dwarf is good for the female dwarf.
So, beards. The initial function of beards may have been protection from cold, neck protection, some combination of the two, or something additional. If it was for protection from cold, this adaption clearly came to be sometime before dwarves became subterranean, or at least while they spent a considerable amount of time in cold climates (such as mountain ranges). Anyway, once beards exist, they serve not only the functions they were selected for, but also work as an indicator of health, much like human hair. A long, luxurious beard is an unfakeable sign that a dwarf has good genes, and has had access to good nutrition for long enough to grow that lovely beard. This sets up a selection pressure where a big beard leads to increased mating possibilites with better partners, just like a peacock's tail.
Once this effect is in motion, not only is there pressure to mate with a big-bearded dwarf for their genes, but also because the fact that there is a preference for big beards means your kids are better off in the mating game if THEY have big beards. It feeds off itself. For more on this topic, see (for example) The Red Queen, by Matt Ridley. At some point, the original genetic-showoff function of the beard may be equalled or eclipsed by the fashion-following function. Again, Ridley explains it a lot better than I can.
Anyway, that's why dwarves have beards, both male and female. Also, the idea of tiny dwarven babies being born with beards makes me warm and fuzzy inside, so I insist that they do in fact sprout beards in utero.