he was a tight-fisted hand at the grindstone, Scrooge! a squeezing, wrenching, grasping, scraping, clutching, covetous, old sinner! Hard and sharp as flint, from which no steel had ever struck out generous fire; secret, and self-contained, and solitary as an oyster. The cold within him froze his old features, nipped his pointed nose, shriveled his cheek, stiffened his gait; made his eyes red, his thin lips blue; and spoke out shrewdly in his grating voice. A frosty rime was on his head, and on his eyebrows, and his wiry chin. He carried his own low temperature always about with him; he iced his office in the dog-days; and didn’t thaw it one degree at Christmas.

Note in this passage the author’s use of temperature and season to emphasize his protagonist’s exceedingly unpleasant demeanor: "The cold within him," "his thin lips blue," "He carried his own low temperature always about him," "he iced his office." The phrase "cold hearted" or "cold blooded" is believed to have its origins in Shakespeare’s King John and is synonymous with uncaring, dispassionate individuals, including those who kill without remorse. When Dickens used this language in describing the character of Scrooge, he was emphasizing the extent to which Scrooge was without compassion for his fellow human.

The phrase also refers to Scrooge's seeming immunity to the effects of weather. The text tells us that "external heat and cold had little influence on Scrooge." It also tells us that "he carried his own low temperature always about with him." Essentially, Dickens is telling us that Scrooge's melancholy and miserable mood is a well-established habit; sunny weather has as little effect on his mood as stormy weather. 

Scrooge is so cheerless and asocial that no one stops him on the street to give him a greeting. Women and children avoid asking him for directions or help in any way. Even dogs pull their masters away from him. So Scrooge is an unpopular figure in his town. His unpopularity stems in part from his miserly ways. Scrooge only allows his clerk a piece of coal to heat his work area. As the small piece of coal is insufficient to make a good fire, the clerk is always cold during the winter months. Scrooge hides the coal-box in his own room so that the clerk has no access to it. 

In fact, Scrooge is such a miserable person that he refuses to celebrate Christmas. So, the phrase "no warmth could warm, no wintry weather chill him" also means that Scrooge is continually miserable, regardless of the weather or circumstances of his life. 

Simply put, Ebenezer Scrooge is a cold man. He has a cold heart. He doesn't appear to care about anyone or anything other than his money. As a result, we are told,

"No warmth could warm, no wintry chill could chill him."

This is a use of metaphor. He is so cold, he cannot be warmed. We see him interact with people at the beginning of the story, before the ghosts, where he could have shown empathy, care, and warmth. He does not. We also see where he could be warmed, like with the men who ask him to donate to charity. This is an opportunity for him to be warmed by the struggles of others during the holidays. He is not.

When it says "no wintry chill could chill him," we understand that he is so cold that the winter weather could not possibly make him any colder. He almost seems inhuman.