Narrower tread/higher sidewall is the trick with snow tires. Regular width snow tires for an M3 just ride on top of the snow. You need a tire that gets down and grips.
I run Dunlop Winter Sport 3D 235/40 18's on all four wheels on my DD M3. They're mounted on 18x8 generic alloys. It was a package from Tire Rack. Admittedly, you'll have to rachet back your performance expetations somewhat but you will get through the snow!
Oh, one more thing - the M3 (particularly w/ZCP) has very low clearance. So, if the snow is more than ~4/5 inches you'll be plowing the street!