17" is more of a good compromise between the great handling of our cars and the lower cost on wintertyres. I have had both 17" and 18" on my GTI, and to be frank i feel that 17" are the best solution, (i have 18" atm). you still have the excellent handling of the GTI but relativly "cheap" wintertyres on offer plus i feel with the very white winters we have had the last 3 seasons they seem to grip better in the lose snow.
IMO you should not even consider 16" for the GTI. Buy a cheap car instead for winter use 
I'm with Danish on this one and he has got a lot more experience than most with winter tyres
Last winter I used winter tyres (for the first time) on a 2nd hand set of 17 Monza's; the reasons being I got some cheap, they to tend to come up for sale all the time (except for now!) I wanted to maintain the look of the GTI, the monza's are such an easy wheel to clean, they are OEM so didn't cause any issues with Insurance, we do get snow but not as much as the rest of Europe so I wanted to maintain good grip for dry and wet days, 225 winter tyres offer much greater grip than a normal tyre on the type of snow we get and are a great balance between winter snow use and winter dry/wet use.
My wheels were cleaned and polished (again) in the summer and i will be keeping an eye on the temp and forecast to decided when these go back on the car - probably some time after the half term holidays.
With all the power/torque of the GTI I wouldn't like to run thinner tyres than 225
