All-season tires become hard and loose grip below 7C.
Summer sports tires are even worse. It says on the sidewall what sort of tires they are. J08M3 - If it says summer then BMW is off the hook.
The issue is not just snow. Winter tires are called winter tires because the rubber compound and tread are made for rain, ice, and snow at temperatures down to -15 to -20C. Winter tires are superior even when the temperature is 5C. Once the temperature starts going above 10C winter tires start to wear out quickly because the tires are soft.
You have an expensive car and I know you can afford winter tires. Just get them and use them. It is a pain storing a set of rims and tires but do it. Get 18 inch rims and use winter tires. They will drop your stopping distances in the winter and stop you from rear-ending me!!