In "Winter Dreams," Dexter feels that he has taken a significant step towards achieving his American Dream when he plays golf with the well-to-do.
Dexter notes the significance of playing golf with the wealthy patrons of Sherry Island. When he takes to the golf course with the other men, Dexter recognizes how far he has come in his own life:
He [Dexter] did not consider it necessary to remark that he had once carried Mr. Hart’s bag over this same links, and that he knew every trap and gully with his eyes shut — but he found himself glancing at the four caddies who trailed them, trying to catch a gleam or gesture that would remind him of himself, that would lessen the gap which lay between his present and his past.
Dexter feels a sense of accomplishment. When Dexter looks back at the four caddies, he sees something that "reminds him of himself." He notices the "gap which lays between his present and his past."
For Dexter, he feels that this moment is an important one to achieving his American Dream. He experiences this because he is included with the very men for who he used to caddy. He has "arrived" in terms of being considered part of the wealthy community. He also feels that such a moment enables him to capture a woman like Judy Jones. In Dexter's mind, playing golf with the well-to-do makes him feel that he is on his way to accomplishing his "American Dream."