I can't claim to be inspired by weather, but a blizzard does one thing for me as a writer. I can't leave the house, so I settle my mind and concentrate on writing. There's no rushing to the post office to mail out those fliers that advertise the new book. There's no visiting libraries to make sure every person in the place knows who I am and wants to recommend my book to patrons. There's not even meeting a fellow author for lunch and moaning about the state of the business for an hour or two.
When circumstances force me to drop everything else and write, I find I'm at my most creative, and the work that gets done seems to be my best quality stuff. I often come out of my focused state to find that I've missed a meal or ignored my family for hours on end. Luckily they understand that and don't mind.
I don't know what people do who live in temperate climates. If I were always distracted by good weather, I might never get anything finished. Every once in a while I need a good Michigan blizzard to plant me in my chair and make me write until the plows come home.