As a high-horsepower RWD car that comes with summer tires, the M3 desperately needs winter tires if you are going to drive it through wintry weather. Both the E90 and F80 M3 commonly come with 19" staggered wheels, which makes snow tires hard to find.
In previous years, the Bridgestone Blizzak LM-60 was available in 255/35R19 front and 275/35R19 rear, but these have been discontinued and the replacement does not come in both sizes.
This year, the best winter option is the Pirelli Winter Sottozero Serie II, which is in stock in both sizes. With highly effective brickwork sipes, the Sottozero offers a multitude of biting edges to generate snow traction for accelerating, braking and cornering. With a W-speed rating, the Pirelli tire exceeds the performance potential of most other winter tires. Even performance winter tires usually max out at a V-speed rating.
While the M3's low ground clearance and wide tires will limit its effectiveness in deep snow, an M3 (or M4) outfitted with a set of winter tires can be a surprisingly capable vehicle in moderate snow.
To prepare your M3 for the winter, take a look at the current pricing and availability of the Pirelli Winter Sottozero Serie II.