WELCOME and CONGRATS!
I'm guessing that you have the Potenza SUMMER tires on yours, since yes, even in our state/area, unless you ordered the car with them (and waited a LONG time for it to show up), you do not have the Michelin Pilot Sport all seasons on a car ordered for DEALER stock.
YES, these should not even be driven on in even MINIMAL snow depths.
The Pilot Sports are not too bad in SHALLOW (like < 2" deep) snow, like we got here on the Delaware River this past week.
You probably got a bit more than we did here on the 'coast'?
With the PROPER
winter shoes on this car, it is a BEAST in the snow, even without an added mechanical limited slip diff.