The disillusionment featured in the short story revolves around Dexter's belief that happiness can be attained through gain and want, without some type of moral foundation that serves as a bedrock for all endeavor. In many ways, Dexter's belief in happiness is illusory. As a caddy, he is entranced with the trappings of wealth, and the allure that high society features. When he golfs at the same course for which he used to caddy, he realizes that he is playing in a foursome with the same people for whom he used to be a caddy or a type of servant. His "love" for Judy is one that is based on physicality and wealth. Dexter is entranced with what Judy represents and the world of which she is a part. In the end, when he is told of her sad life and the beauty that is now gone, Dexter weeps because it is the death of his illusions, with only reality left. The disillusion present is one predicated upon firmament that lacks stability.
"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.
In many ways the same disillusionment is present in Fitzgerald's other works, particularly in Gatsby. But Dexter is the main sufferer of disillusionment at the end of this story, and he holds on to his version of the American dream through a number of obstacles. He reaches a level of success that allows him to catch the eye of his childhood fantasy girl Judy Jones. But even when he reaches that level, he finds that there is some emptiness to the dream once he finds the rather empty and ugly character of Judy underneath her glittering exterior. He doesn't lose his faith in the vision until he finds out about Judy's rather wretched life at which point he acknowledges the utter emptiness of his "American Dream."