[Vast Buffalo Wing Conspiracy]

AFAIK, the appendixes never state that Dwarf women grow beards. It says that there are few of them (about one third of Dwarf population), and that they are so much like to male Dwarves, that non-Dwarves mistake them for male Dwarves. However, nowhere does it say that Dwarf women have beards.

Tolkien left this ambiguous, so let us do a little basic deduction. Tolkien says that Dwarves are jealous of their "rights" - ie, they are highly protective of their women and don't like to expose them to outsiders or potential rivals. He also says that Dwarf women seldom travel, and by implication, they travel in disguise as, and among, Dwarf men. In other words, Dwarf women are secluded from all other men except their husbands and relations, and when forced to travel, for reasons of secrecy and security, they travel in disguise. Disguising them as Dwarf men is a simple enough ruse to avoid undue attention from non-Dwarves.

This is just my own deduction, but I have always assumed that when forced to travel, Dwarf women went in "drag", as it were, with false beards, and thus easily passed themselves off as males to non-Dwarves. It's not that they naturally grow beards, but that they can easily disguise themselves as male Dwarves if need be, because non-Dwarves have seldom seen Dwarf women and so can't spot the disguise.

This is my own interpretation, of course. But it does not conflict with what Tolkien wrote about Dwarves.

[Overtaxed]

It says that there are few of them (about one third of Dwarf population), and that they are so much like to male Dwarves, that non-Dwarves mistake them for male Dwarves.

Maybe they wear false beards when abroad? Seems to me a Dwarf without a beard would stand out.