In Pride and Prejudice, nature serves to a minor, almost insignificant, extent as a minor, static character in that nature, in several instances, helps move the plot forward. It is minor because it helps the major characters, and it is static because nature does not change in personality or character.
Towards the beginning, rain serves as a character because it drives both Jane and Elizabeth to remain for a time at Netherfield. When Jane is invited to dine with Bingley's sisters at Netherfield, Mrs. Bennet thinks up the grand, manipulative scheme of sending her there on horseback in the rain. Jane catches a cold and is too ill to be transported back to Longbourn. Bingley invites her to stay and be medically treated at Netherfield. Elizabeth also hurries to Netherfield to watch over Jane and keep her company. This gives Elizabeth many opportunities to have conversations with Darcy, and Darcy begins to realize that he is "in danger" of feeling quite attracted to her (Ch. 11, Vol. 1). Hence the rain is responsible for first drawing Elizabeth and Darcy together and awakening his feelings.
Rain shows up as a character again after Elizabeth first meets Wickham and just before the Netherfield ball. It is important because the rain prevents her from immediately further getting to know Wickham, whom she is becoming attracted to (Ch. 17, Vol. 1).