As a young man, Dexter is ambitious and determined. He dreams of being more than just a caddy. He has "winter dreams" of a better life. The narrator adds that he is not a snob, but he does have a desire for an upper class kind of life:
Often he reached out for the best without knowing why he wanted it---and sometimes he ran up against the mysterious denials and prohibitions in which life indulges. It is with one of those denials and not with his career as a whole that this story deals.
Dexter had this urge to reach out for something better or something higher. Perhaps, this is simply his understanding of what it means to reach for the American Dream. He associates Judy's looks and money with the upper class and the glittering world of his aspirations.
Judy's looks fade as she gets older. When Dexter learns of this, he comes to the realization that her beauty is/was superficial and fleeting. Likewise, the glittering world of the elite social class she belonged to also became quite superficial to him. Dexter has an epiphany that this once evocative, fantastic world of his dreams had always been superficial, shallow, and fleeting. It leaves him feeling empty that this dream is gone now because he sees that there was never any substance in it.