This is a really fascinating question. We must start by defining heroism. For the purposes of this answer, I will define it as acts of moral courage. A hero would be someone who has firm beliefs about what is right and who is willing to take serious risks in pursuit of the right. A hero would not waver in the face of danger.
Given this definition, it is clearly difficult to be a hero in a totalitarian society like this one. The society tries its best to prevent people from having personal opinions and thoughts. However, being a hero is all about defying the odds and fighting difficult battles. Heroes are not made in soft and easy circumstances.
I would argue that heroism is possible in a totalitarian society, but it is (of course) very difficult. Winston starts out to be a hero but he really is not the stuff that heroes are made of. He tries, but he succumbs to fear in Room 101. Presumably a tougher person would have succeeded in resisting the pressure.
History is full of people who have managed to be heroic as they resisted totalitarianism. Heroism is possible, but Winston and Julia just aren't made to be heroes.