Good choice to go for winter tires. When you buy them consider the extra $50 per season ($100 / yr) to put them on and take them off.
There is another option that you should strongly consider. It will even save you money and save your mags.
Put steel rims on for winter. I would also return to a normal size for winter. For example, if I did the math correctly all the sizes below are equivalent to your 225/50/17:
225/55/16
215/60/16
215/65/15
In fact, the standard size on the G6 is 215/60/16. At the VERY LEAST downsize to 215/55/17 to gain more traction on the snow/ice.
But just to prove the point (prices are from the link above)
4 Blizzak tires in 215/55/17 = $448
4 Blizzak tires in 225/50/17 = $552
4 Blizzak tires WITH rims 215/60/16 = 564.
Option 3 (tires and rims) is the most economical. You will save your mags (no winter dammage), and they will cost MUCH less to install everyyear (you save the mount and balance, only pay minimal fee for install). The 215's will also give you better traction than the 225's because they are narrower (more pressure on smaller area so cut through snow better and don't act as a "ski" on looser powder).