While the narrator is the protagonist in the story, it is the Italian major who is the hero. He has the qualities typical of a Hemingway hero: he is an accomplished sportsman (champion fencer) and is a decorated soldier. But what really makes him the hero in this story is his role as the narrator's mentor. The narrator doesn't know until the end of the story that the major is teaching him a lesson. And, maybe the major doesn't realize this either.
One day, during rehab with the machines in the hospital, the narrator recognizes the major's stoic lack of confidence in the machines and his lack of hope for a full recovery. In a subsequent hospital visit, the major asks the narrator if he is married. He replies 'no,' but he intends to. The major becomes irate, calls him a fool, and after a tirade, storms out. He comes back, calm and collected, and apologizes, saying he just learned of his wife's death. The story ends with the major ignoring the pictures of the rehabilitated hands, and instead, staring out the window. What he teaches the narrator (inadvertently or purposefully) is that, in spite of the possibility of losing something - a loved one or a limb - you must keep going. When the major stares out the window, ignoring those supposedly encouraging pictures of healed hands, he is sort of staring into the void (or the window to the battlefield) and embracing life even with its potential for loss. This is bravery. This is what the narrator needed to learn.
This theme reminds me (somewhat) of Camus' "The Myth of Sisyphus," where he implores the reader to imagine Sisyphus as happy. After being destined to push a rock up a hill only to have it fall each time, for eternity, Camus says that since Sisyphus perseveres despite being aware of the futility, he is superior for it. The difference here is this: Camus' hero is admirable because he finds meaning in an absurd situation. Hemingway's hero is admirable because he finds courage in a situation (life and the war) where there is meaning and happiness, but also where loss is possible and in some cases, (like death) inevitable.