If you plan to keep the car for a while, yes, invest in a set of 17" rims & tires.
For winter, you're going to be looking at 225/45/17 all the way around. For the power of the 335i, I would suggest minimum H-rated, such as the Pirelli Sottozero Serie II, Dunlop Wintersport 3D, Yokohama W.Drive, etc...
If you want low cost, Hankook W300 icebear are on clearance.
I can help you out with any tire questions you may have.