For Dexter, seeing himself as "newer and stronger" than the wealthy people to whom he compares himself is in reference to Judy Jones. As he recognizes the "men who had already loved Judy Jones," Dexter rationalizes that he can succeed where these men have failed. In his mind, Dexter will be more successful in his wooing of her due to his stock of strength. He understands that these previous suitors were wealthy, reflective of "old money." Dexter, though, sees himself as a form of "new money." With his growth and emergence into wealth from humble beginnings, Dexter believes that he is "newer" and "stronger" in comparison to the traditional wealthy people that have failed to capture Judy Jones' attention.
For Dexter, this rationalization is the basis of why he thinks he can hold onto Judy. He believed himself to be made differently, offering her something that previous men could not. In this, one can see the optimism that Dexter has towards his "winter dreams." This hope and unbridled sense of opportunity serves as his motivating force, rooted in the idea that he, Dexter, is "newer and stronger."
A distinction is made throughout this excellent story between "new" wealth achieved by someone with "questionable" roots such as Dexter Fletcher with his middle-class background and the "old" wealth of the upper-class that is inherited and not earned. At the beginning of the third section, Dexter compares himself to the other admirers flocking around Judy Jones and recognises his own superiority, yet also identifies the central paradox associated with his "winter dreams":
He had seen that, in one sense, he was better than these men. He was newer and stronger. Yet in acknowledging to himself that he wished his children to be like them he was admitting that he was but the rough, strong stuff from which they eternally sprang.
The paradox is that although he is better than the other suitors precisely because of his drive to succeed and his ambition, caused by his humble origins, he wants his children to have that elegance and confidence that being born to an upper-class family gives. In society, children who are born wealthy are regarded more highly than the newly-rich.