Not only is the miserly Scrooge impervious to the needs of fellow humans, but he is also insensitive to the deprivations of Nature itself. Indeed, this description of him is symbolic. Scrooge is not fully human.
I think that post #3 has figured it out. Dickens has used the cold and the fact that it does not bother Scrooge to symbolize how cold hearted he is. The transformation that Scrooge goes through during the book is shown in the change not only in his disposition but also in the weather near the end.
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!
When Charles Dickens opens his novel A Christmas Carol, one of the details he includes in his exposition of the main character is that Scrooge's bad mood and ill disposition are not affected by anything, not even the weather. Scrooge is such a cranky old man that the beggars do not ask him to "bestow a trifle" and children will not ask him what time it is. He is the same person, rain or shine: a cantankerous old man whose only reason for existence for years has been to make as much money as possible and spend as little as possible. We find out during the night of time travel with the Christmas ghosts how Scrooge developed into this unhappy person, and ultimately how he will be transformed.