Depends where you are in the UK for sure.
If you have a lot of roads with snow/ice/slush especially with hill work, winter tyres make a decent amount of difference to the traction / stability and overall safety of the car.
I've run 18 inch winters on seperate rims for years and they are fine, it offsets the summer boots too.
The only problem with not getting them before the snow hits, is the prices go crazy.
For most of the UK you'd do fine with All Seasons but they are a compromise for the summer AND winter, so why bother on a GTI?