Hold the pony there lone ranger. While snow tires like the blizzak or better all-purpose tires like the triple tread assurance will beat the stock eagles, I wouldn't go around saying that stock setup absolutely blow and should be illegal.
having lived in NE AND in NorCal, i can tell you that tahoe winters are lot worse in terms of road conditions (mountain passes, steep grades, etc) and that being said I've done a lot of research in the Mazda3/snow driving category.
the truth is, if you want good traction and spend a lot of time in snow, go AWD. if you really want a mazda3, then forget dropping loot into entirely new wheel/tire combos that look like sh#$ when you're going to be using chains most of the time anyway. I would look at chain alternatives like spikes spider. you improve traction significantly over what any tire alone can offer, you don't have to buy ugly ass and small steel wheels, and even better you will save a lot of money.
i have spikes spider on right now for the entire winter. it cost $300, took 30 minutes to install the hardware, and each time i need to use chains, it takes me a minute to put them on. worth every penny. i used them for the first time during the huge snowstorm that hit tahoe this past new year's, and my little 3 was literally kicking the crap out of audi a4s and 4x4 broncos who drivers seem to think they are invincible to ice.
just my $0.02