I have had no issues in the past few years driving a 2006 Z4 and a 2009 135i.
My only issue is finding the right winter tires. My 135 currently has Dunlop WinterSport 3D which I bought from Tire Rack. I am not that happy with them, since the ice traction is not great, but the snow and warm weather traction is pretty good.
Would you recommend getting Blizzak's or another type of winters for an M3?