I know just how you feel Satch! I remember correcting yours when someone told me there's no 'n' in Satch! Put down the pitchforks and torches, people. It's called satire.
Your ability to drive the M3 in the cold winter is not just a function of whether there is snow on the ground. In cold weather your summer tires will not grip the road. Get a spare set of wheels and a proper set of winter tires and then just drive the thing. I live in Chicago and took delivery of an E92 M3 coupe in the winter of 2008. It's glorious year round -- snow and cold notwithstanding.
protect the M3 It would not be worth ruining the rims or risking a slide off the road---you have a great winter car, protect the M3! (I don't think any M3 driver would allow run flats?). I see mine parked in the garage for several months and it is frustrating (Syracuse NY) but once a week I sit in it, start it (always starts right off) and roll it back and forth to change the tire burden. Patience and protection (think of the salt damage!) will pay off and extend the life of the M3. I just took delivery of a 2011 Audi S5 to assuage the lack of the M----it's a great car but it's not an M3.....
A car isn't much fun to own if you can't enjoy it with confidence On the other hand, I understand your concerns. As far as the wheels are concerned, there are number of wheel cleaning and maintenance products out there. I'll leave it to the detailing evangelists on here to make any recommendations or endorsements, but your road wheels can be protected by a variety of means. I think you should have the last word in how you use the vehicle. Sliding off the road is a driver education issue, and the BMWCCA has an "app for that." It's called HPDE (High Performance Driver Education). It's definitely a higher level than the driver's ed classes that we slept through in high school, but it's not fender to fender road racing either. Instead it is exactly what is says: High Performance Driver Education. It's not meant so much to survive an accident as it is accident AVOIDANCE. Such as how to safely steer out of a slide, and some of the really stupid stuff human beings might do in a panic that could actually make the situation worse (such as letting OFF the brake when you feel the ABS pulsing during a panic stop - instead you want to keep your foot firmly pressed down until the car's motion completely ceases and comes to a safe stop). IMHO, the stuff they teach in these HPDE's is something that ought to be taught in driver's ed everywhere. Instead, they only teach you how to pass a monkey-simple DMV exam -- and we pay for this with the carnage on our streets and highways
BMW does have a great driving course, but you can still loose your rear wheel drive car--or any other--by hitting a patch of black ice--no matter how much training you've had the guard rail may be in wrong place---why risk the M3 when you've got a winter car...
The NorthEast was granted a beautiful few days this past week and the M3 got plenty of exercise. I plan on leaving the M3 as is for the moment and learning more this summer (perhaps an HPDE course) and see how I feel about it next fall. My X3 has new winter shoes and raring to get some real deep snow. Either way I am in BMWs good hands.
FWIW, there are ice driving schools, both club and pro. There aren't a lot of them around (Badger Bimmers held their last one about a decade ago), but if you persevere, you'll find one. I got 'drafted' to teach in ours because 1) I drove a Quattro and 2) one of the organizers said I knew how to do a 'Scandinavian flick' turn. After opining that I didn't exactly know what the hell that was, he told me that he'd seen me flick the wheel in and out to get the tail out for a countersteer/oversteer slide. Oh ... THAT. So we did a day on frozen-solid Lake Sinissippi and I actually learned something new: that left foot braking works in a Quattro almost as good as it does in a FWD. I still struggle with the theoretical 'Why', but I now know it works - for some reason.