snow tires is a must and the M3 should do fine w/ them in the snow.
when i had my Audi A6 w/ performance tires, i was sliding everywhere in the snow. but when i put snow tires on it was a whole new experience. full traction w/ quattro and snow tires means lots of fun in snow conditions.
i am currently driving a C55 w/ snow tires and it performs quite well. C55 has almost 370 hp so i would think it will be similar to the M3.