Hawthorne uses both direct and indirect characterization to disclose the character of the Reverend Mr. Hooper. Direct characterization is the actual physical description of the character. We find direct characterization right after Hooper comes out wearing the veil, causing quite a commotion among his followers.
Mr. Hooper, a gentlemanly person, of about thirty, though still a bachelor, was dressed with due clerical neatness, as if a careful wife had starched his band, and brushed the weekly dust from his Sunday's garb.
Indirect characterization is the disclosure of the character's behavioral traits. The idea is to elicit the reader's opinion and to invite the reader to make conclusions and to infer from the text the actual mental state of the character. Based on the way that the young reverend carries about with the veil, with his want to preach about secret sins, and the fact that he dedicates himself entirely to this pursuit, leads the reader to conclude what is the actual personality of the reverend.
We could argue that he is eccentric, but we could also call him sanctimonious; after all, would he not be considered a sinner too? He is dedicated, stern about his values, and someone who is willing to give up everything and everyone to make his point. All of those descriptors, however, are not directly explained by Hawthorne. It is the character itself, the actions that we see, and the reaction that the character instills in the other characters in the story which produces the indirect characterization of Mr. Hooper.