I think that its important to think about weather when you are going to live somewhere for a few years, but it shouldn't be the ultimate factor.
For undergrad I moved from a warm climate to a very cold and snowy one. I lived there for 4 years and I loved college. If I had let that one thing change my decision I would have been at a school that I probably wouldn't have liked as much.
Now to be fair. When I graduated I moved as far south as possible, for the weather. When I applied to PhD programs I thought about the weather. It wasn't a huge factor but I looked harder at schools in warm climates and the coldest i applied to was Nashville.
Is it important? Yes. A deciding factor? No.