While walking on ice, one should take small steps to avoid slipping . This is because smaller steps to avoid sliping . This is because smaller steps ensure

There is a critical angle   for the leg where if exceeded the foot would slip. The less the available friction the smaller the critical angle. 

Even without ice, try to walk on a dirt path using a really long stride and when your foot pressed down when the leg is at a high enough angle away from vertical it will slide. It is the same reason it is not recommended placing ladders on high angles or they will slip.

The secret is that you don’t need friction to run on ice, only perfect balance. Friction is only needed for acceleration and deceleration. Because when the normal force is parallel to the impact force there is no need for friction, and you can balance the direction of the impact force so the average direction is parallel to the normal force.

μ=tan⁡(cθ)" id="MathJax-Element-1-Frame" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;" tabindex="0"> without ice, try to walk on a dirt path using a really long stride and when your foot pressed down when the leg is at a high enough angle away from vertical it will slide. It is the same reason it is not recommended placing ladders on high angles or they will slip.