You should be fine
I have driven a 1993 Crown Vic, a 1999 Crown Vic, a 2005 Crown Vic and now my 2008 Charger. I absolutely had to have a set of dedicated snow tires back in CT with the Vics.
With the Traction Control, the Weight of the Car, a full-size spare (and the donut) in the trunk and perhaps a bag of kitty litter, I have not needed to get dedicated winter tires for my Charger; I'm just using the OEM all-season GY ComforTreds. Unfortunately, this past winter with multiple blizzards here in Northern VA, my car had to sit because ground clearance was more of an issue than traction.
Most winters we tend to get more ice than snow, in which case you might as well park it, cause nothings important enough to mess up the Charger