2006 Toyota Corolla Grinding noise when on ice or slick pav

Do you have anti-lock brakes? MAYBE it is just normal on icy road or black ice. When driving on black ice or slick road and you step on the brakes, you can hear one tire at a time stopping (skidding) for a second, then rellease again. Each tire won't lock stop continously. That is why it is anti-lock brakes, your car won't skid that much on black ice.

Only 29000 miles, I do not think it is the brake pads but you can get it check out. If brake pads are worn out, grinding noise is continous when you step on the brakes whether on icy road or not. It is a metal to metal grinding sound.

At 29000 miles, I believe your car is still under warranty. Try calling the Toyota dealer.