This is an interesting topic because once you notice Fitzgerald's use of seasons, you can appreciate how he and other other author's use the "year of life" metaphor in their writing. The year of life metaphor conceptualizes a life span as a year; a year that starts in the spring time when all of the earth is reborn. Young adulthood is early summer. Middle age is later summer. Old age is fall. Death comes in winter.
To make this fit into the structure of the novel, you have to consider the metaphor a little more carefully. You have to think about Gatsby and his relationship with Daisy as being a "life." He met Daisy in the spring time of his life; he is reunited with her during a beautiful summer in West Egg. The relationship reaches its climax on the hottest day of the summer: the night of the big showdown at the Plaza and the subsequent death of Myrtle. The aftermath of those events plays out in the fall of his life; he is killed on a day at the end of summer; he remarks that the pool hadn't been used all summer, and his funeral takes place on a day that evokes the beginning of autumn. Nick leaves New York by October to return to his roots in the Midwest. Gatsby died too young and never actually reached the winter of his life, but his prime was past when Daisy rejected his love for her and his dream ended.