Answer: It explains why Bob does not recognize his friend Jimmy when he talks to the policeman.
In the story, Bob walks along with the man who claims to be Jimmy for a while, and they even start to share experiences, before he realizes that man is not actually Jimmy. Bob only notices it when they step into an area that has better light and that allows him to examine the stranger's face more carefully.
The weather also has a secondary purpose, which is that of setting a sad, bleak tone to the story, foreshadowing a tragic ending.