I still have relatively new 15" winters (195/65/15) from my old VW Jetta.
I was told by one dealership that these should work fine on my 2012 Madza 3 Sport GS. I just needed to buy 15" steel rims.
Another dealership said, no...I needed to go to 16" tires (205/55/16).
My understanding is that the thinner and smaller the tire, the better it is in snow. Then again, I'm in Toronto, so I doubt it would make that much of a difference, given the amount of white stuff we get.