Infographic by Tablet. Falling on ice leads to many injuries and even 60 deaths a year in the USA (about the number that will die due to tornados). The graphic encourages thinking like a penguin. Penguins walk well on ice (in some ways) and they also fall well.
Seeking to keep your weight well supported (short strides) is wise (and sliding instead of picking up your feet can help). Falling well is also important. It is basic physics, you want to lower your center of gravity if you are start to slip and avoid any excessive force (so sliding is better than trying to stick out your hand and support all your weight). The elderly are especially susceptible to injuries – avoiding taking direct shocks to the wrist, knees or hips is wise). It does seem kind of silly to learn how to fall but it is very helpful in avoiding injuries.
On sidewalks if you are going to fall and there is snow piled up off the sidewalk, falling into the pile of snow may well be softer than falling directly onto the sidewalk.
On ice you have lower friction so strategies that require friction are not useful – quick moves often rely on very sturdy bases (which are based on the friction of our shoe on for example concrete [which normally is good - though business shoes are not very good] and on ice [where it is very poor - sliding and gradual moves are better]).