I'm afraid I'll have to disagree, unless you define the hero as the main character. Since he's just about the only character in the story, he would "win" on that account.
But his behavior is not heroic as I see it. Instead of facing his fears, investigating the visions/stories/whatever he experiences/ to see what is "real," he assumes that what he experiences in the woods, and remember it's not clear that he experienced anything, is true. If he were in any way heroic, he would have fought through these experiences to see what was true, and then acted upon what he found.
Instead, he takes the role of a coward, believes the "easy" things he thinks he saw in the forest, and that faliure destroys his life.
Nothing heroic here.
In my opinion, Goodman Brown is indeed a heroic figure in the story "Young Goodman Brown." Goodman Brown confronts situations and characters who would have been terrifying to anyone, which takes a tremendous amount of courage. In observing the frightening scenes he finds himself encountering, Goodman Brown exhibits a great amount of bravery and self-control, which are certainly heroic traits. Throughout all of this, Goodman Brown maintains his sense of right and wrong, his ethics, and his "innocence," each of which is indicative of a true hero. Turning away from wrong and persevering as a moral man who is true to himself is heroic.
As the question states, it is possible to argue either way on this question. The support that you give your argument is what is most important.
Let's look at a few well recognized heroes. Captain America, Spider-man, Luke Skywalker, and even Beowulf are all characters that use violence to fight against the forces of evil. They are all young, white males, and each character has special powers that make each character able to successfully fight against a great evil. Each character is loved by the public for his heroic acts, and each hero saves helpless innocents from being hurt or killed. Goodman Brown can't claim any of those things other than being a young, white male. He goes off into the forest by himself. He is shown that everybody he knows and loves is a servant of the devil, and he returns a broken and scared man. He didn't physically fight anything, and he didn't rescue anybody either. We are told that Goodman Brown became "a stern, a sad, a darkly meditative, a distrustful, if not a desperate man" after his night in the forest. He even "shrank" from his own wife. By the time he dies, he has pushed everybody away from him, and his gravestone is left blank.
. . . they carved no hopeful verse upon his tombstone, for his dying hour was gloom.
While Goodman Brown may not resemble the physically strong and violent hero type that is common in the media, I believe that he exhibits other heroic qualities. I do believe that Goodman Brown is brave. He goes off into the forest, at night, to speak with the devil. He chooses to do this. He's not being forced into it through blackmail or anything like that. Additionally, Goodman Brown's bravery is bolstered by his confidence in himself and his faith. Readers are told that Brown's resolve was "excellent" and that he felt completely "justified."
I also see Brown as a hero because he maintains his sense of right and wrong. He doesn't give into the devil's arguments, and he doesn't join up with his wife and the rest of the townspeople. He stays strong in his faith, and he doesn't allow the forces of evil to win him over. What I want to point out is that Goodman Brown had to keep up his fight on a daily basis for his entire life. He is surrounded by people that have given into the devil, and Brown must continually work to maintain his personal faith in God. In this way, Goodman Brown is a hero based on his strength of character.