"Winter Dreams" was a preliminary sketch of The Great Gatsby in that Fitzgerald worked out some main ideas and character development in the story that would make their way into the novel. There are strong similarities between Gatsby and Dexter, as well as between Judy Jones and Daisy Buchanan.
Gatsby and Dexter are both born into a lower social class they reject and into poor economic circumstances they strive to overcome. As boys, neither of them accepts his identity, and both of them work hard to make themselves over into different people. They are ashamed of their personal backgrounds. Jimmy Gatz goes so far as to actually change his name. Dexter, like Gatsby, misleads people as to where he was born.
Dexter and Gatsby both watch rich people to learn how to speak, dress, and act in their world. Dexter becomes better at this than Gatsby did. Gatsby tried to "act rich" but set himself apart--by his garish display of money--from those who really had been born to wealth.
The dream motif lies at the heart of each work. At heart, Gatsby and Dexter are both romantics rather than realists. They live (and in Gatsby's case, die) for their dreams. Gatsby dies with his dream intact, still waiting for Daisy to call. Dexter continues to draw breath, but with the death of his romantic illusions, to him his life no longer seems worth living.
Here is a good eNotes resource that discusses this question in detail.