I live in Denmark where swapping to winter tyres/wheels is commonplace. On my Mazda 6 wagon I run 225s on 17" rims in summer and 205s on 16" rims in winter. No prblem with brake clearance. The winter tyres are higher profile than the summers, yet still have a slightly lower overall diameter. This over-estimates my speed and distance travelled by about 5%. I do about 10k km per year on winters, so not that significant, but worth considering.
I bought my tyres / wheels online from a German shop and probably paid about £600, including shipping. Worth it, to be honest, with snow on-off for four months of the year.
It's probably worth checking the speed and load rating of any tyres too. I got the same as my summer tyres. Frequently drive at 100 mph or more (not in snow, of course) here and in Germany (wife's parents house) so it's good peace of mind.
Gotta say, if you expect snow, winter tyres are fantastic. My car happily stops, starts and drive through 6" of snow with no problem and brakes well on snow / ice with little ABS action.
Finally, it's expensive, but I save on wear on my summer tyres which happily live in my shed over winter. Actually plan to swap over tomorrow as temps are set to move to single digits soon.