Just follow this route:
http://************/3dznh3
Driving through snowy and mountainous Colorado is not that bad at all even with summer tires.
If I could do it with a Peterbilt, I don't see why you can't do it with a BMW.
FYI: Peterbilt 367 has 14 additional tires compare to your BMW 335i.
The trick is "Don't go too fast on sharp turns".