As been posted: invest in good snow tires instead. E.g., Pirelli Scorpion Winter tires are excellent.
VWs drive great on snow with the right tires. If it's deep, you can deflate your tires a little for added grip.
As you already realized yourself: chains are tricky on AWD vehicles. If you don't chain all four, you might still end up skidding all over the place because power cannot be distributed independently in the front and rear. I live in the Alps and honestly, I've never seen someone putting chains on an AWD vehicle. Chains are a pain in the ass, only work for short distances, while winter tires are virtually free because you don't use your summer tires during this time.