Tai Chi Walking 

  How to walk safely on slippery ground

The main problem is that your forward momentum puts much more force in a forward horizontal direction when the front foot strikes the ground.  Normal walking is quite efficient: on a flat path we recover about 65% of our energy by planting the front foot and letting our momentum carry us forward and over it.  In a normal walking gait, every step is actually a forward fall, caught by our front foot as shown below.
  


But, if there is no friction to hold the front foot it shoots forward, and driven by momentum and your weight pressing into the skidding leg, down you can go.  In the image below, a front mis-step and slip is simulated:



Ideally, you can use "Tai chi walking" to reduce the horizontal slipping force to nearly zero.  You balance on one leg while the other reaches out "empty" with no weight.  When the front foot touches the ground you smoothly transfer your weight from the back leg to the front leg: the force in the front foot is almost straight down.  When all your weight is on the front foot the empty back foot is picked up and gently moved to the front, placed on the ground, and the cycle repeats.  This image below shows the slow and exaggerated stepping movement from the Tai chi form.  Although the step is large, there is no forward push on the front foot, or rearward push-off from the back foot.



This may sound complicated but you did it all the time as a kid: "walking tiptoe" we called it.  Whether you touch with the toe or the heel first the important thing is that there is hardly any weight on the foot when it makes contact.