[Perfectlap]

well for a snow tire to work its best the narrower the better.
And of course smaller tires are much cheaper and you more choices.
You need the same type on all four corners. The light front end of the car is going to struggle to find traction regardless of what's going on in the back if you go with all seasons in front only. That can be dangerous.

Changing tires is not as expensive as buying a whole new set of wheels/tires but it's still not cheap. Some discount places won't touch an expensive Porsche wheel for fear of scratching the paint with their low end machinery. And the places with the proper machinery can be expensive. A mid level place charged me $170 to mount my Summer tires. They see those 18" Porsche wheels and I see $$$ in their eyes.