I've got a 328ci stick shift. I've driven in 3 relatively harsh snow storms in Long Island, NY this year. Riding on 17" Toyo TS-1s. Yup, you'd think I'd be sliding all over the place...
But the way I've handled the winter without snow tires is by having two 60 lb bags of sand in the trunk. You definitely need that extra weight in the back for the tires.
But then again, my commute consists of mostly flat level roads. I'm not sure how it would handle hills, but so far, the sand bags seem to work great!!
Give it a shot. Only a few dollars per bag at Home Depot.