Dude dont put your life in jeopardy. Get a set of snow tires. Very easy to find a used set on criagslist. I would NEVER drive a BMW with all seasons ever again. I tried that one winter bad idea.... Hit a patch of ice, jumped the curb and ended up between 2 trees somehow. Pick up a set of blizzaks new and put them on stock wheels its not worth the risk.
Heres some examples
try and buy his