Dexter is a dynamic character, meaning he changes in a significant way by the time the story ends.
Most main characters in a story are dynamic, because most stories involve meeting challenges, reacting to them, and being changed by them in some important way. In other words, the main character or protagonist in a story is not the same person as he or she was when the story began. Somehow, that person thinks differently, sees the world differently, or has developed a significantly different personality.
If a character is the opposite of dynamic--static--that means he or she experiences no significant changes; that character basically stays the same from the beginning to the end of the story. Minor characters are usually static: the ones who aren't that important to the story. Sometimes, a main character is static in a story because he misses out on a chance to change.
Getting back to Dexter in "Winter Dreams," let's see what makes him a dynamic character by examining his character traits near the beginning of the story versus toward the end.
How he is near the beginning of the story:
As a young teenager working as a caddy at the golf course, Dexter is hardworking and competent: he never loses a ball, and his boss calls him "the best caddy in the club." Although the narrator doesn't explicitly say so, we believe Dexter has been doing this job for quite a while, so we assume he's also reliable. At the same time, he's deeply affected by the changing of the seasons and is often overcome by melancholy. We can tell how deeply emotional he is, too, because he reacts so impetuously to meeting Judy for the first time, suddenly throwing away his caddy job:
"But he had received a strong emotional shock, and his perturbation required a violent and immediate outlet."
And, notably, Dexter describes himself as a boy as "proud" and "desirous." The narrator adds that Dexter operated under the illusion that Judy was desirable, so we also know that Dexter was easily enchanted, or full of illusions.
As the story goes on, Dexter grows up, becomes successful in business, plays golf, and suffers endlessly from his on-again, off-again relationship with Judy. Because he wants to possess beautiful things, he keeps on chasing after the beautiful Judy no matter how many times she hurts him.
Now let's take a look at how he is at the end of the story, as a result of all those life experiences:
Is Dexter still hardworking, competent, and reliable? Yes. He's one of the richest young men in the country, it seems, and he's worked his way into a higher social class. So, that aspect of his personality hasn't changed.
Is he still melancholy and impetuous, given to fits of sadness and sudden emotional displays? Yes. Look at that scene toward the end with Devlin, when Dexter loses his cool when he hears what happened to Judy.
Is Dexter still enchanted? Is he still blinded by illusions? No. He has lost his illusions; he understands the reality now that Judy is not some perfect, ever-gorgeous being. She's become a frumpy housewife and isn't even pretty anymore. Dexter realizes this, and then he realizes that he's become disillusioned, finally. That's how Dexter changes. Here's how he acknowledges and laments that major change:
"Long ago," he said, "long ago, there was something in me, but now that thing is gone. Now that thing is gone, that thing is gone. I cannot cry. I cannot care. That thing will come back no more."
To sum it up, although Dexter retains many of his basic personality traits, his life experiences cause him to build up and then shatter his own illusions. His way of looking at the world changes from enchanted (and unrealistic) to realistic. That's how he changes, and that's why he's a dynamic character.