1985 Trans Am Tire Question

Hello, I have a really dumb question. I own a 1985 Pontiac Trans Am with a 305 engine. The car has only 21,500 miles on it. She runs like a dream, is regularly maintained and is stored in the winters. Everything on the car is original, including the tires. My question is this. Should I get new tires? The tires are not close to being bald, but my mechanic said that I should replace the tires because the rubber is too hard and could slip on slick surfaces. I'm not the most mechanically inclined person in the world, but I always thought that tires get replaced when the thread become close to bare. I have never heard of rubber becoming too hard. Thank you for your assistance