I'm going to throw a little different (controversial?) idea in there and say that the cold weather could actually serve to symbolize Scrooge's coldness as a human at the beginning of this iconic holiday novel. Perhaps this is the reason why the cold doesn't affect him! Someone so heartless, ... so cold, has no reason to react to the physical cold of winter. Notice how the frigid weather is hardly even mentioned at the end of the novel. Why? The focus is on Scrooge's transformation coupled with the warmth of Christmas. Further, the coldness (of both setting and character) at the beginning of the story further contrast with the beautiful warmth (again of both setting and character) at the end of the story. Ah, the charm of Dickens!