I currently drive a subaru and we are a pretty hardcore snow crowd. Love putting the car sideways!!
It is common opinion Nokians are some of the best snow tires out there. Just my .02 Not suer if they have sizes to fit the mazda - but you should really get 16" steelies or cheap rims for winter(since 15" don't seem to fit). The extra sidewall will do wonders for snow traction.
The roads where I live are packed snow/ice, have been since november, will be till probably end of april/may. I still use my crappy Bridgestone RE92s, with a little care most tires will work fine in most conditions, it's all about the driver. ( I have over driven conditions and slid into a few soft snow banks - (no harm to car

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