Having somewhat suddenly and rather dramaticaly ended his job working as a caddie at the golf course where he met Judy, Dexter clearly sets himself on a course to greatness. This is shown through his decision to go to an older and more respected university, which is also more expensive, rather than a newer, less prestigious (and therefore cheaper) university. What Dexter determines he will achieve in life is not simply the kind of lifestyle that is associated with the rich and famous, but the possession of wealth itself, as the following quote makes clear:
He wanted not association with glittering things and glittering people--he wanted the glittering things themselves.
How Judy embodies his "winter dreams" is that she, in the text, is described to be one of those "glittering things." Note the repeated reference to gold in her dress and appearance. It is clear that Fitzgerald presents her as being one of those objects of great wealth and desire that Dexter associates with success and the American dream, and with her breeding and attitude, she becomes the centre of his focus as Dexter seeks to be successful.
At the beginning of Part II of Fitzgerald's short story, the narrator suggests that Dexter Green has "winter dreams" of not just achieving financial success, but he dreams most of all of "the glittering things themselves."
Because of his dreams, therefore, Dexter selects the "precarious advantage" of a prestigious university in the East from which a degree will help him attain the "glittering" people and things. Later, after Dexter graduates and starts a small laundry that specializes in washing woolen golf-stockings and sweaters, he is soon running a string of laundries throughout the country. Before he is twenty-seven, Dexter owns a chain of laundries in his section of the country.
Then, one day when Dexter is twenty-three he is given a guest card to the Sherry Island Golf Club for a week-end. There he encounters Judy Jones, who has become "arrestingly beautiful." Because Judy represents to Dexter the grace and beauty of wealth:
This color and the mobility of her mouth gave a continual impression of flux, of intense life, of passionate vitality--balanced only partially by the sad luxury of her eyes.
After seeing Judy, Dexter seeks her as the ultimate "glittering thing" of his desires. Her actions on the golf course and her later invitation to dinner give Dexter a "new direction to his life."