What was Tolkien's stance on ladybeards?
Basically, nothing much was said because of Tolkien's general gynophobia. Especially because dwarves were fairly blunt and industrious and generally displayed masculine traits. Wouldn't want any empowered females outside the nobility ruining one's notion of a perfect pre-industrial world...
We can resolve this by using a bit of armchair evolutionary biology. What is the function of the beard? If we could somehow determine that, we can make predictions about whether all dwarves will be bearded. This assumes beards are adaptations.
etc. etc. etc.
Technically, as humans evolved out of hairy apes into creatures that had less hair, we can assume that the adaptation was to grow
less hair.
Although still controversial (as it was caught up with the Feminist movement largely only because a woman proposed it,) the "Aquatic Ape" theory states that humans lost their hairy body (where hair would keep them warm) in favor of more fatty bodies because they started becoming dependant upon rivers (and their fish) as a source of food as the Desertification of the Sahara began, and humanity's ancestors were forced out of the trees. Hair is generally useless as an insulator when wet (excepting extremely oily hair, like a water dog's), and fat was a better insulator.
If there is any historical evolutionary parallel to dwarves, however, it would actually be the Neanderthals. Neanderthals were cousins of humans who left Africa earlier than other humanoids did (and so were cut off from the full evolutionary progression into humanity), and were generally shorter, broader, more muscled, and tougher, but also not as efficient a long-distance runner (thanks to the shorter legs).
Because of this, they were better adapted for colder weather and forests like Europe had during the Ice Age, and were better adapted to be ambush hunters, while humans were better adapted for warmer grassy plains. While humans hunted by traps or throwing spears, Neanderthals hunted by hiding behind (or in) trees, and leaping down upon megafauna like a wooly rhino's back, and then repeatedly beating it to death with a spear, hopefully before the wooly rhino could toss him off and trample his stupid ass to death for grappling with a critter that outmasses him 10 to 1.
In short, there are many parallels between dwarves and Neanderthals (and I'm honestly not sure why more people don't notice this...)
So then, the question is, "do Neanderthals have beards the same way humans do?" The answer to that is, essentially, yes. They were generally hairier (and probably more women had chin hairs or thin mustaches than human women do,) but there was a male/female difference according to every mockup I've seen. In fact, this article here:
http://www.independent.co.uk/news/science/his-name-is-a-common-term-of-abuse-its-time-neanderthal-man-got-a-better-press-argues-colin-tudge-1601789.html actually argues that the beard of a pre-historic human was actually the equivalent of a peacock's feathers or a stag's horns - they are how males attract females by asserting their fitness to mate through growing one.