I'm going to get a set of winter tires for the upcoming terrible weather. I know a lot of people are running 245/40/18 but can I run 225/45/18 instead? I've heard that running a narrorer winter tire will give you better contorl on snow. Is that true?

 

I have 245/40/18 summers, but am running 225/50/17 for winter. A narrower tire is better in snow.

 

I ran 225/45-18 Wintersport M3's last year on OE 123 wheels and they worked well.

For this winter I bought a set of ASA wheels, also 18 x 8, from member price9195 (replaced his 550 w/ a 335i) and they had 235/45-18 Wintersports already mounted. They are a little taller than stock and look nice filling up the wheel wells -- no rubbing even with being lowered.

 

I think that the idea is to leave room in the wheel well so the snow does not build up. You get better traction when the snow can escape from the well.

 

I ran 225/45/18 as well last year.

Even with the 245/40/18 there wouldn't be any build up in the arch.
The idea on winter tyres is to have them as narrow and small (in wheel dia) as possible for better cutting abilities through snow and slush and less chance of aquaplaning and the smaller wheel, higher side wall for more flexibility in the tyre also aiding grip when you need get going.