I think I got the answer. I guess it wasn't the SRT-8 version with the 20 inch wheels.
I looked on the Tire Rack website, and they recommend either 17" or 18" wheel/tire sizes. You might just try getting 17 wheels specifically for installing winter tires. There seem to be decent options, and most aren't that expensive as long as you stick with 17" tires. Something like a Bridgestone Blizzak DM-Z3 235/65QR17, which is really designed for pickups/SUVs.
If you go up to 18" wheels, your tires are going to be more in the performance winter tire category, with lower ice traction. I don't know how fast you drive, but if I had a powerful rear-drive car in a Michigan winter, I wouldn't push it.
Again - I'll just say again that maybe the original poster might want to reconsider driving this car when there's snow on the ground and a decent chance of ice. I remember seeing that Youtube posted video of sub-zero temps in Portland, Oregon. With ice on the ground, many cars just skidded on an inclined, icy surface. The Volvo AWD SUV got moving somewhat, which made it even worse because the driver couldn't control it. There was a rear drive BMW (probably w/ summer tires) that kept on slipping and sliding when power was applied.