Tone is the way an author looks (implied or stated) at an audience or a subject in a text.
The tone in Hawthorne's short story "The Minister's Black Veil" is one of doubt. Mr Hooper dons the veil in order to test the faith and acceptance of his parishioners. Prior to wearing the veil, Hooper's parishioners thought him to be self-disciplined and rational. Once he begins wearing the veil, his parishioners, wrought with dismay, begin to turn against him. The rumors behind his reasoning begin to run rampant.
By wearing the veil, Hooper shows that people are easily swayed by things they do not understand or cannot comprehend. Therefore, the tone of doubt shows Hawthorne's (through Hooper) inability to trust in society and the way their beliefs waiver.
In addition to the dark and gloomy tone pointed out by other commenters, this story is also characterized by an immense sadness. Hawthorne validates Mr. Hooper's belief that each of us hides a secret sinfulness that we want, at all costs, to prevent others from suspecting; Mr. Hooper believes that we not only hide our true selves, then, from others, but we also try to hide from ourselves and even God. When Mr. Hooper gives his first sermon wearing the veil, his congregation seems to acquire some inkling of its meaning, and this causes them to distance themselves from him. It is too painful for them to think that he might have an accurate understanding of their souls. Further, when Elizabeth, Mr. Hooper's fiancee, figures out what the veil symbolizes, she blanches and runs from him, never to return again. These responses seem to show that Mr. Hooper is correct. And if he is correct, then this means that none of us ever truly knows or is known by any other human being, including, perhaps, ourselves, and this is an incredibly sad and isolating notion. In his final moments, the parson says,
"When the friend shows his inmost heart to his friend; the lover to his best beloved; when man does not vainly shrink from the eye of his Creator, loathsomely treasuring up the secret of his sin; then deem me a monster; for the symbol beneath which I have lived and die! I look around me, and, lo! on every visage a Black Veil!"
Therefore, since Hawthorne validates Mr. Hooper's behavior, it means that Hawthorne must, on some level, relate to Mr. Hooper's terrible sadness as well. The idea that we are all trying to hide our true selves means that we are all, voluntarily, alienating ourselves from everyone else for the entirety of our lives. Our need to hide the very thing we all have in common means that we can never really know anyone else or be known by them. This terrible irony is tragic and helps to produce the story's sad tone.
It is important to remember that "tone" in literature refers to the author's attitude towards the subject or theme of the story. That means that readers must look for ways in which the author presents his attitude or perspective through descriptions and word choice. Take the following passage about the Parson's sermon on the day he first wears the veil as an example for finding words that show attitude:
"It was tinged, rather more darkly than usual, with the gentle gloom of Mr. Hooper's temperament. The subject had reference to secret sin, and those sad mysteries which we hide from our nearest and dearest, and would fain conceal from our own consciousness, even forgetting that the Omniscient can detect them."
Based on some of the words in this passage, the tone presents a feeling of dark and gloomy secrecy. There is also a sense of mystery and confusion as to why the minister wears the veil and refuses to take it off. Look at another passage for similarities and differences in the word choice that creates tone:
"All through life that piece of crape had hung between him and the world: it had separated him from cheerful brotherhood and woman's love, and kept him in that saddest of all prisons, his own heart; and still it lay upon his face, as if to deepen the gloom of his darksome chamber, and shade him from the sunshine of eternity."
There are some positive words in this passage, but they are about all the things Parson Hooper misses in his life due to the veil he wears. Truthfully, the tone does not change throughout the story. The tone remains dark and gloomy to the bitter and lonely death of the parson. This gloomy tone might move readers to think about what they place before their own lives that blocks out happiness and keeps darkness in. The story is quite depressing.