In "The Minister's Black Veil," does Mr. Hooper's smile symbolize anything?

I agree with the previous answer. I do not believe that Mr. Hooper's smile is symbolic of anything. The veil is the predominant symbolic image throughout this story.

Mr. Hooper's smile is not an emotionally happy smile, though. In fact, it is frequently described as "sad." The smile is also described as "faint" several times. Hooper is not grinning ear to ear with pleasure. His smile is a smile of irony. He knows the reason that he is wearing the black veil. It is symbolic of secret sin. He also knows that every other person also wears his or her own metaphorical black veil. Hooper smiles because he knows that there is a sad irony in the fact that the people in his town do not understand the meaning of the veil.

Hooper constantly has a faint, sad smile that glimmers beneath the veil because he's witnessing similar naivete. People don't publicly acknowledge their secret sin, but it will be exposed in the afterlife.

A sad smile gleamed faintly from beneath the black veil, and flickered about his mouth, glimmering as he disappeared.

What does Mr. Hooper's smile symbolize in The Minister's Black Veil?

The minister's smile represents his knowledge of the secret "moral truth" of the people around him. As he says on his deathbed, every face, to him, is wearing its own veil; he means that everyone around him, while appearing virtuous, is in reality wearing a mask or concealing their true identity. His smile can be understood as a recognition of that insight.

Another way of thinking about the smile is to see it as a response to the way people change in their treatment of him. The veil in this sense becomes a kind of silent accusation; people steer clear of the minister because there is something judgmental about the veil. The minister's smile, in this case, is in response to the hypocrisy of these people, who were friendly to the minister before the veil but now are afraid.

A third way of thinking about the smile is as an honest expression of relief or pleasure. The veil in this sense is a kind of "lens" or filter that allows the minister to see into the hearts of those around him; the smile here could mean that he feels relief and gratitude at this insight into others and that, in separating himself from them by wearing the veil, he is preserving his own moral uprightness.