Good question! In Fahrenheit 451's first section, Montag encounters Clarisse walking around in the rain. When running away from the mechanical hound near the novel's end, Montag asks Faber to turn on the sprinklers in the hope that the hound will lose his scent. In each instance, rain, though artificial in Faber's case, is associated with characters who value meaningful conversation and independent thought. Rain then symbolizes rebirth and redemption, for these are characters who Montag wishes to emulate. Rain here is also juxtaposed with the central, destructive element of fire, which helps establish an opposition between Beatty and the other firemen and Clarisse and Faber.
Montag's trembling reveals his deep, at first subconscious anxiety. With his trembling, he begins to realize that he is uncomfortable in his occupation of book burning, and that he will soon be forced to decide between continuing to burn books or to break the law and collect books himself. It also represents his constant fears, first that something is wrong with his life and then later that he will be caught with the books.
Finally, the color grey represents the dull, lifeless character of the world Montag inhabits. Grey is the color of overcast or stormy skies and thereby represents bleakness, sadness, and cold. Compare this image to the colorful image of multi-colored flowers blooming in spring! The constant portrayal of Montag's world as grey is juxtaposed with the color of his hidden books: "He kept moving his hand and dropping books, small ones, fairly large ones, yellow, red, green ones." For Bradbury then, books bring warmth and comfort into the world.
For further information, please check out the eNotes guide to Fahrenheit 451!
According to the author of How to Read Literature Like a Professor, rain can either represent the character's inner mood and thoughts or it can symbolize a catharsis--a new beginning for that character. When Montag is running for his life away from the hound and toward the literates who have memorized books for a future time, it is raining. It probably is a little of both--Montag has lost his life as he knows it, his wife, and he has murdered his former boss. He probably is a little depressed about all that despite the fact that he is now free. The rain is also a catharsis for him--he has to be looking forward to a time when he can talk about the past and books he's read and his hopes for a future with books and freedom of thought/speech.
Trembling and the color gray are also signs of depression or inner turmoil.