Winston is not a traditional hero. He is full of self doubt and he doesn't win in the end. However, he shows bravery first through questioning the world he lives in and not accepting it as others do around him. Once he begins to question, he takes action, although it is not on a large scale. However, he does go against Big Brother knowing how terrifying the results might be. How many people could say they have knowingly and readily faced their worst fear for what they believed in who who they loved?
In the end, he is heroic not in his accomplishments, but in what he attempts to accomplish. This is one case where the act of rebellion is more important than the result of the rebellious act.