The answer above is excellent and provides many details in the analysis of the role of the seasons in Morrison's novel. I will simply add some thoughts on the framing of the novel.
In The Bluest Eye, Morrison uses a variety of motifs to link parts of the novel to her overall theme. The seasons are one of these motifs since, as explained above, the nature of the seasons highlight the events that occur during those seasons.
Another interesting point about the seasons in the novel is the order in which they appear. Normally, the progression from autumn to summer would suggest a death and decay to renewal and blossoming process; however, the progression of the novel is much the opposite. Morrison toys with the readers general acceptance of the nature of the seasons to suggest that society's general acceptance of the standards by which we live are problematic.
Each section of the novel offers a glimpse at one aspect/time of Pecola's life. Essentially framed around one year of her existence, the novel describes the events season by season, often ironically juxtaposing Pecola's reality with the traditional symbolism of the season.
The novel begins in autumn, which may seem unusual for some who would expect it to begin with spring. However, autumn is a time of harvest, of ripening, and therefore of coming into maturity. Although this is not true for Pecola in this section, she witnesses Claudia's and Frieda's growth, and learns from that. Also, fall can become a time of new growth for those who attend school, since the new year traditionally begins in the autumn months.
"Winter" is perhaps the most aptly named of all the sections. Winter traditionally symbolizes cold, barrenness, sterility, and even death. In this section, we are drawn deeper into the infertile ground that is Pecola's life. The scene with Geraldine and her son Junior shows just how far Pecola is outcast from her society. She is surrounded on all sides by hostility and hatred, as further evidenced by the Maureen Peal episode. Even when Pecola attempts to be friendly, she is cast aside, leaving her alone and empty.
Spring traditionally represents growth, new life, change, beginnings, etc. However, in the novel it is the most ironically named of all the sections. Instead of change and positive transformations, Pecola only experiences more and more abuse and terror. Her mother beats her, her father rapes her, and no one offers a hand or a kind word. Frieda also experiences abuse at the hand of Mr. Henry. Spring is also traditionally a time of moving forward, looking fondly on the future. Yet in this section, we look back on Cholly and Pauline's lives, seeing the horror and pain from the past which is transferred now onto Pecola.
Finally, summer is a time of relaxation, freedom, vacation, etc. We typically associate it with children out of school, but it connects back to the idea of harvest in the autumn. The summer would be the last time to relax before the rush of reaping in the fall. But instead we are left with a broken, clearly insane Pecola, wandering the town on her own. There is no redemption for any character, and Claudia leaves us with the image of Pecola as the scapegoat for the town, the one on whom everyone else washed themselves clean.