If you really want to run or walk on ice and not worry about falling, these will do it.  I have used these to run on our nice icy roads in our unsalted neighborhood.  They grip better than I ever imagined they would.  The cleats dig right into the ice.  Note:  I'm fat so that might help with the digging into the ice.  I could run full speed (slow) and stop on a dime, never feeling like I was slipping.  They do collect slush and some snow between the rubber and your shoe, but anything designed like this will.  The sport version has a strap that goes over your shoe.  As long as you buy the right size, they will not slip off your shoe.  I wear a size 12, which is as big as these go and they fit my running shoes perfectly, and I was even able to pull them over some lightweight boots so I could keep my feet dry running.  They're pretty comfortable as long as you stay on snow or ice.  On cement, you can definitely feel where the cleats are through your shoe.