This article is from the Tolkien Newsgroups FAQ, by Steuard Jensen firstname.lastname@example.org with numerous contributions by others.
[This updates question V.D.1 of the Tolkien FAQ.]
Yes. The most canonical evidence for this comes in Appendix A,
where it is said of Dwarf women that
They are in voice and appearance, and in garb if they must go on a
journey, so like to the dwarf-men that the eyes and ears of other
peoples cannot tell them apart.
It seems that (male) Dwarves in Middle-earth all have beards: among
other evidence, as Bilbo sets out on his adventure in _The Hobbit_, we
read that "His only comfort was that he couldn't be mistaken for a
dwarf, as he had no beard." Given that, the quote above must imply
that Dwarf women were bearded as well.
However, we do not need to rely on such implications: Tolkien
answered this question explicitly in other texts. In _The War of the
Jewels_ ("The Later _Quenta Silmarillion_: Of the Naugrim and the
Edain", written ~1951), Tolkien wrote that
no Man nor Elf has ever seen a beardless Dwarf - unless he were
shaven in mockery, and would then be more like to die of shame...
For the Naugrim have beards from the beginning of their lives, male
and female alike...
In _The Peoples of Middle-earth_, Christopher Tolkien says that a
similar statement was present in an earlier draft of Appendix A as
well. As these statements are entirely in agreement with the canonical
evidence cited above, the conclusion that Dwarf women had beards seems