From the description that Hawthorne gives of the veil, it seems to hang down in front of most of Mr. Hooper's face. It does not seem to be a veil that a woman would use, necessarily, because it is, of course, not only black, but sort of a make-shift veil that he threw together himself.
"Swathed about his forehead, and hanging down over his face, so low as to be shaken by his breath. . . it seemed to consist of two folds of crape, which entirely concealed his features except the mouth and chin, but probably did not intercept his sight, farther than to give a darkened aspect to all living and inanimate things."
The word "swathe" means to wrap up closely like a bandage. Good thing the villagers saw him come out of his own house because they could have mistake him for a robber or bandit! The word "crape" is actually an Anglicized word from the French word "crepe" which is defined not only as a French pancake, but a band of silk or cotton fabric that has fine crinkles in it. So it would seem as if he looked like a cross between a bandit and a woman in mourning; except for the fact that parts of his mouth and chin could be seen.