This is an interesting question, since the novel is often interpreted as a good example of determinism, seeing Ethan as a victim, rather than a hero--someone whose life is determined by forces of nature and society beyond his control.
However, he does model the classic tragic hero in some respects. As a young man, Ethan did not enjoy power or high social position, as do classic tragic heroes, but he was a good man, remarkable in several ways. Ethan was young, strong, and very intelligent. He was curious and inquisitive by nature and longed for an education. Sociable by nature, Ethan dreamed of living a larger life than Starkfield could offer, one of excitement and fulfillment. Therefore, he left Starkfield to pursue his dreams.
When interpreted as a tragic hero, Ethan has a fatal character flaw that causes his downfall and destroys his life. It is personal insecurity. When Ethan left school to come back to Starkfield to care for his sick parents, his plans were interrupted, but his dreams were still within reach.
The turning point in Ethan's life, the moment when his tragic fate is sealed, does not occur until he marries Zeena. After his parents' were both dead, Ethan could have sold the farm and returned to his life in the outside world. He did not. Instead, he marries Zeena, a decision dictated by the flaw in his own character. Ethan marries to keep Zeena respectably under his roof only because he doubts his ability to survive the loneliness of living in the isolated farm house throughout the long and brutal New England winter. Ethan's personal insecurity--his lack of faith in himself--sets into motion his downfall and eventual destruction.
When Mattie comes into his life, Ethan then struggles to reverse his fate, as do all tragic heroes. He tries desperately to effect his and Mattie's escape from Starkfield; when that fails, he steers their sled into the big elm, trying to effect their escape from living lives without each other. He fails in both attempts, and he is destroyed. The terrible irony for Ethan as a tragic hero is that unlike other tragic heroes, he does not die a physical death, experiencing instead a spiritual death as he drags himself, both literally and figuratively, through the remainder of his tragic life.