Definitely not. The way in which the protagonist remains nameless throughout the entire short story is our first indication that he is not a hero. Secondly consider the way in which the man is shown again and again to be incredibly arrogant about his mastery and dominance over nature, and refuses to acknowledge the terrible danger of nature and its power over man. The man in juxtaposed to the dog, who is aware and respectful of nature, throughout this tale to reinforce this. Note how the man's feelings of nature are described towards the beginning:
Fifty degrees below zero meant eight-odd degrees of frost. Such fact impressed him as being cold and uncomfortable, and that was all. It did not lead him to meditate upon his frailty as a creature of temperature, and upon man's frailty in general, able only to live within certain narrow limits of heat and cold, and from there on it did not lead him to the conjectural field of immortality and man's plce in the universe.
This quote clearly indicates the lack of respect that the protagonist has for nature at large, and hints at his arrogance which will actually result in the protagonist's death. There is no way, therefore, in which this protagonist can be considered a hero. He ignores the advice of those more experienced than him and is blind to the signs of nature, happily plunging into a very extreme situation resulting in his own death.