No need to put specific routines for NPCs ; they could behave like in daytime, just cycle the lighting and atmosphere.
This plus bad weather are very important for immersion and sense of time going on, even it's only cosmetic it will add plenty to general feeling.
Plus things like rain could also affect items and surface behavior like fire being easier extinguished, creating mud and water puddles to be frozen, etc.
Things that can affect battle outcomes and add or remove options. Offering more stealth to anyone, reducing visibility (game already able to deal with smoke and fog), all little gameplay things that will greatly add to gameplay variations as well (and add replayability for instance), offering more variables in the surroudings.