Winston is not exactly heroic. He is an "Everyman" character, a common man. He tries to be heroic, but he obviously fails. In this way, he is more like an anti-hero (one who lacks heroic attributes). In the end, of course, he is caught and tortured; he becomes an "unperson"--by definition, not heroic.
Look at his name: Winston Smith. Yes, his Christian name is "Winston," after Winston Churchill, the great British hero the age. This might sound heroic, but his surname is "Smith," the most common name in the English-speaking world. In this way, Orwell wants him to be the working class everyman who is defeated by the superior powers of the state. The novel's theme focuses on the death of the individual.