My Vette is parked for the winter, is there a tire care product that I can put on the tires that will keep the tires conditioned all winter long?

Do you park your car inside in a garage? I am guessing you do...I use the Black Magic silicone product on my tires all year long but I live here in the South.

Yes the car is parked inside garage.

I would stay away from oil or silicone based products. When it penetrates the rubber it could cause cracking and some nasty discoloration.