Run a comparison of your f30 winter wheels & tires with the winter size wheels/tires for the f06 at this site to get an idea of an idea if there will be any major difference in "inset" & "poke" (inset towards suspension parts...and poke toward the fender):
www.willtheyfit.com
Thinner winter tires are usually recommended for driving in deep snow...the thinner tire allows it to "cut" through the snow & contact pavement or road surface. This would need to be remembered during cold/dry periods...that your tires are narrower thus slalom type driving won't be quite like normal with your summer "wider" tires that have more contact with the pavement.
I've used narrower than recommended winter tires on several BMWs...and had no issue as long as the wheel/tire specs stay within the same range as the overall diameter/circumference of the BMW recommended tire size. My e38 740iL series recommended winter tire was a 235/60/16...and i used a 225/60/16. And I also ran a narrower winter tire on my e39 540iT...I ran a 215/50/17 winter tire and I believe the recommendation was 235/45/17 tire.