You know the saying that in spring, "a young man's fancy lightly turns to thoughts of love"? Well, this is a story about a young man and his thoughts of love, but as the title tells us, it is certainly not set in spring.
All of Dexter's fantasies about a brighter future come to him during the bitter Minnesota winter instead of the spring and summer, when the poets tell us we are supposed to daydream. Basically, Fitzgerald is slapping us across the face and telling us that he's doing it differently. So take that. This is a new kind of story about dreams, different from the classic poetic associations between dreaming and spring.
For more on the symbolism of the title "Winter Dreams," check out our section on "Symbols, Imagery, Allegory."