Do they make low profile SNOW tires?

I live in Northern NY but my dream car is a Ford Mustang Cobra R. I want to get just a normal mustang and make it a Cobra R replica, but it'll be my daily driver. So do they make snow tires in low profile?

And don't tell me to get a different vehicle just because of where I live. I'm set on this car and am just looking for an answer to the question asked. Don't act like my mother.

Just put some crownvictoria wheels on it in the wintet

Low profile is rather a bad idea in winter as ideally you want an extra inch of ground clearance. I'd agree. Get a set of steels for winter. Michelin Alpins are significantly better than regular road tyres and widely available. But for me the best are the vredstein wintracs. Just outstanding. They are winter road tyres not deep snow knobblies. In this car more than a couple of inches of snow isn't going to be do-able. And put 50kg of sand/salt/paving slabs in the back in winter or you'll never keep traction.

Yes. THEY make low-profile winter tires and have for decades.

Whether the Cobra R is for the '90's or the "00's simply stick with the OE tire size. And yes, most all tire manufactures will have snow tires in that recommended size.