"Winter Dreams" just like The Great Gatsby is one of Fitzgerald's diatribes against the Old Money class in American society and its seeming false offer of equality to those who believe in the American Dream. In the story, Dexter observes the wealthy golfers for whom he caddies and believes that if he works hard enough, he can one day be just like them. He envisions scenes where he drives up in luxurious cars and the wealthy surround him simply to listen to him speak.
Dexter does work hard and becomes wealthy, but once he makes it to the top, he realizes that the dream has become corrupted (just like Daisy is the corrupted version of Gatsby's dream and can never live up to his expectations).
Both of these works present Fitzgerald's frustration with his own life and attempts to achieve the American Dream. He, like Dexter and Gatsby, became interested in a wealthy socialite (Zelda) and was looked down upon by her social class and family. When he finally did win Zelda and marry her, he endured a tumultuous relationship with her where their wealth was unstable and their faithfulness to one another questionable. He believed (as he demonstrates in "Winter Dream") that the Old Money portion of society corrupts the moral, decent Midwesterner.