Get a winter tire/wheel pkg at the minimum. Something like a 235/55-17 to get some sidewall height. Limiting factor is ground clearance over the plow-mounds of snow.
In New England, lots of folks used to drive beater full-sized RWD Caprices, Crown Vics etc. with not too many problems as their "salter".
For me, I'd get a junky little front-driver for the bad days, and save the "Stang for the nicer winter days when the roads clear and dry out a bit. Winter / Snow Tires