Hi,
I spent 1 month with my GTi in the Alps a couple of years ago in conditions ranging from full ice to 40 cm of new snow with Summer Tyres and Snow Chains. It was a NIGHTMARE.
I had the super expensive Weissenfells Clack and Go Quattro snow chains that fit 19inch alloys. They fit on the tyre differently to normal snow chains, without requiring the chains to be clipped round the back of the tyres, and were 'easier' to put on and didn't scratch the face of the wheel at all but ... in reality snow chains are only really good for short journeys in deep snow.
I ended up on multiple occasions putting the chains on in freezing blizzards, searching for one snow chain that had fallen off that I only discovered once I'd got to the bottom of a valley and almost didn't make it back up the other side, getting very close to skidding off the side of a 500m cliff and driving through variable conditions ranging from 40 cm of snow then in to tunnels with no snow etc etc. All the while every other 2WD car cruised by with snow tyres on as if there was no snow at all.
My advice would be to fit snow tyres and then have a back up pair of snow chains (the expensive ones if they're within budget). I also drove a van in a ski resort for 5 months with snow tyres and I only had to put chains on twice, both times to get out of a snow drift. The rest of the time snow tyres were fine.