I've just ordered an F20. It will be my 4th BMW and the first that I will be putting on winter tyres. I had an e90 which I drove on summer tyres all through the snowy winter that we had 2 years ago here in the UK. Driving was a bit like snowboarding as it was more a case of controlled sliding rather than driving. At the time we also had and e82 and it was undriveable compared to the e90.
By far the worst car that I have ever owned for driving in the snow was an Audi A3 sportback TDi with DSG. That was last winter and thankfully we only had 1 day with a light dusting of snow. However, for the first time in nearly 20 years of driving I had to abandon the car due to weather.
On a 116 a winter tyre package including 16" steel wheels can be bought fairly cheaply so it's a no brainer in my opinion. Things get a bit more complicated (bloody expensive) with the bigger engined cars due to the bigger wheels required for brake clearance. I still think it's worth it though. If you don't have them then please just leave the car at home as I don't want you sliding out of control into my nice new car.