I suppose no one wants to be struck by a stray lightning bolt in a thunderstorm, but the Hercules and Xena folks tell me there is almost always cloud cover there. A good dark day shouldn't be wasted. And there's nothing like a wet, misty day to darken everyone's mood. I'm not saying Method acting is the way to go, but it would help if people were already feeling dreary and gloomy when they have to film what is perhaps the gloomiest part of the story. He keeps our senses wide awake.
Movies sometimes add a nice variation in weather to show the passage of time.
Of course, rainstorms in the movies are often mechanically produced with water trucks and hoses, but nature is sometimes put to work to save on time and effort. There's nothing like a good thunderstorm to provide footage of a good thunderstorm. More difficult to work into the schedule will be snow. The only snow we actually encounter in the book is that which falls on Caradhras, the mountain the Fellowship attempts to cross to avoid going near the Gap of Rohan and Isengard. Although this is not a critical part of the story, many people expect to see it in the first movie.