So how would a veil hide the fact that a dwarf is female?
Depends on the style of the veil, to determine how much of the face is covered.
If we put them in a niqab, that would conceal beards.
So, you would be able to tell that the dwarf is a woman, but you would not be able to tell if she had a beard or not.
The suggestion that a culture that used face veils would also think to have masked helmets is not implausible.
As far as women disguising themselves as men for travelling purposes - even with the best disguise, the voice is always a give-away. I have a bunch of female friends who use beards in various costumes, and (not shockingly) many of them are mistaken for men when they wear them...until they speak

Something to keep in mind, if we ever do have traveling female dwarf characters to worry about.