Keep your knees loose. Extend arms to the side to keep your balance and increase your gravity center. Keep your hands out of your pockets, so you can break your fall with your hands if you start to slip. Spreading your feet out slightly— like a penguin— while walking on ice increases your center of gravity.
When we walk, our legs' ability to support our weight is split mid-stride. To walk on ice, keep your center of gravity over your front leg. Take short steps or shuffle for stability.
If you fall backwards, make an effort to tuck your chin, so your head won't hit the ground. Also, try to form a ball and relax the muscles. You will injure yourself less if you are relaxed. Also wearing a heavy, bulky coat will cushion you if you should fail.