Think about it this way. If you have 4 snow tires on another set of wheels, you'll want them on if the forecast is for snow. But the other 95% of the time when it's dry or rain the car will drive like crap with the snow tires and you'll want to put the stock wheels/tires back on. Just do a search on here to see how many people bounced off a curb or got into a fender bender trying to drive in bad weather. The LS1 with an A4 is not good at all in the snow. If you do $1000 worth of damage and jack up your insurance then the beater 4x4 is a better solution. Or just find a friend with 4x4 when it snows or stay home.
