If you have to drive your Crossfire in snow and you live in an area that will get more than two snow storms a season then I think you should consider snow tires.
Regarding driving an automatic in the snow, if you are trying to stop and find the front wheels skidding, either downshift the transmission (just hold it to the left and it will select the lowest gear) and it might help. If you start to fishtail then you should move the transmission into Neutral until you can steer out of the fishtail, unless of course you are like me and you want to see how far you can drive sideways down the road. Don't take my current location into consdieration, I grew up in Connecticut and know who to drive in the snow. I prefer a front wheel drive in the snow but with the right tires I would imagine the Crossfire would be okay to drive.
I don't know if the person that put the blizzaks on, put them on all 4 or not but I would also recommend putting snow tires on all four wheels. Yes it is much more costly but it will provide a lot more control both steering and braking.
Good luck and the next snow storm head on over to an empty parking lot and get the hang of loosing control and getting it back.
If you are going to have your Crossfire for more than one year then I would purchase another set of wheels and keep the snow tires mounted so then you could just switch them yourself, if that's possible.
PS check
www.tirerack.com and read some reviews on various snow tires, this is where you don't want to buy the cheapest tire out there, you want a good quality SNOW (not all season) tire.
PPS a good quality snow tire (unless you're driving on the frozen tundra all the time) will only last two seasons.