The all-season goodyear tires that came with the car are completely inadequate for driving on snow (even packed urban snow). The car is difficult to control and fishtails on virutally any incline.
I believe that without a different set of tires this car is not safe to drive with any snow on the road.
That's hardly anything ground breaking. Since when does any car roll of the lot with tires suitable for snow. If you have any amount of snow at all where you live, then get a good set of winter's. It's not worth risking your life over for a few hundred dollars.
A footnote to my comments regarding the tires on the mazda 3.
I replaced the tires with Bridgestone blizzak's and the car now handles well in the snow.
As an alternatives, if you aren't living in snow country, you can get by with a better set of all-season tires such as the Michelin Pilot Exalto A/S. The Badyear Eagles RS-A are definitely bad tires for wet or snow condition!
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