Dexter is not ambitious just for the sake of making tons of money. The narrator of "Winter Dreams" is careful to remind us that there is nothing "merely snobbish in the boy" (2.1). Dexter is an idealist: he associates cash with the graceful, attractive lives of the members of the Sherry Island Golf Club. In fact, making money is almost secondary to his main ambition of leaving behind his humble origins and joining the upper class. (Take, for example, his embarrassment: "His mother's name had been Krimslich. She was a Bohemian of the peasant class and she had talked broken English to the end of her days. Her son must keep to the set patterns" [3.2].) Dexter dreams of starting a new family, in which his children won't have to worry about being of the right class or stock. Money is a way to make that better life possible, but it's not a goal in itself.
Dexter's effortless financial success allows Fitzgerald, as a writer, to downplay the difficulties of earning money. That way, "Winter Dreams" can focus instead on the major emotional problems that accompany business ambition.
Dexter's ambition does him more harm than good. After all, he ends up miserable and alone.