During the cold Minnesota winters (and we mean cold – trust us), when the golf course is frozen over and Dexter can't interact with the upper class people he envies, all he has left are his winter dreams. These dreams are the metaphor that Fitzgerald uses to refer to Dexter's ambitions for the future. In section one of "Winter Dreams," Fitzgerald writes:
October filled him with hope which November raised to a sort of ecstatic triumph, and in this mood the fleeting brilliant impressions of the summer at Sherry Island were ready grist to his mill. He became a golf champion and defeated Mr. T. A. Hedrick in a marvellous match played a hundred times over the fairways of his imagination, a match each detail of which he changed about untiringly – sometimes he won with almost laughable ease, sometimes he came up magnificently from behind. (1.4)
Dexter's specific dream in this case is to play golf with Mr. T.A. Hedrick and win. Beating a rich dude at golf is his big dream? Well, yeah, but it's more about what it would mean: if he could do it, Dexter would have really, truly joined that wealthy world he only observes from a distance as a caddy.
And remember, these dreams become more and more "ecstatic" as the winter continues. As the winter gets colder, Dexter gets more excited about what the "brilliant impressions" that summer will bring. The fact that Dexter's imagination only runs wild when he is not actually hanging out with the people he caddies for in summer is a pretty good hint that his romantic ideals about the rich life are not based in reality. Being rich isn't all that grand, it seems.
Dexter's winter dreams are fantasies. They have no real grounding in truth – much as Judy Jones' beauty does not necessarily reflect her character underneath the surface. The final proof of this contrast between Dexter's winter dreams and reality comes at the end of the story, when Dexter appears to have achieved everything he has ever wanted. But he has lost those dreams of grace and beauty that he used to have as a boy in Minnesota.