Why do we take small steps while walking on ice? 
When we walk on ice we should take small steps. Small steps ensure: 
a.)larger friction. 
b.)small friction. 
c.)larger normal force. 
d.)smaller normal force.

The correct answer is smaller friction. 
But I think that small steps give larger normal force and more the normal, more the friction.
When we take small steps while walking on ice, do we ensure smaller or larger friction and how?
 A: The reason for small steps is that the lateral forces are decreased.  Imagine taking a large step on concrete.  When you first put your foot down well in front of you, it will be pushing forwards on the concrete.  At the end of that step when that foot is well behind you, it will be pushing backward on the concrete.  The larger the step, the larger these forward and backward forces.
Your ordinary shoes on ice can only sustain small forwards and backwards forces before they slip.  To avoid slipping, we take smaller steps.
A: The problem is that the question is ambiguous.
In controlled, skating rink conditions (with no skates on), what you are concerned about is slipping and balance. Thus, friction is king.
In real life outside the skating rink, on a river or a pond, you are afraid of breaking ice and drowning. Real ice is inhomogeneous in quality and thickness, and there is always deadly water underneath. Small steps ensure that you don't create large normal force against a piece of thinner ice (like a beam with one end supported) and if you do, the sound of creaking will promptly alert you to move back.
A: The art of walking on ice is to plant your whole shoe sole on the ice and just add so much horisontal force to each step that you don't lose your grip. Small steps make this easier and if you lose your grip you have room for a large corrective step to get back in balance. It’s like balancing a pencil on your finger - the further it gets out of balance the bigger correcting motion you need. If a corrective step doesn’t work, sliding is an option. It helps to bend the knees slightly and keep your feet a bit wide.
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.
A: There is critical angle $\mu = \tan( \theta_c) $ for the leg where if exceeded the foot would slip. The less the available friction $\mu$ 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.
To the answer is really that small steps equals gating with angles which minimize lateral loading. The question is worded horribly, as answer b) should say minimize lateral forces.
A: This question is answered using three bits of knowledge:
1) Under pressure, the ice melts to form a layer of water which is eventually the reason why ice is so slippery. (There is a middle ground between the cause and effect which has to do with the anomalous behaviour of water between 273K and 277K. There is a video by Richard Feynman where he discusses this to some extent.))
2) The force applied by your feet on the ice is actually proportional to the tangent of the angle made between you foot and the ground between each step. Furthermore, in order to reduce the force per unit area applied by your foot on the ice (which thereby causes the ice to melt and thereby reduces the friction), you need to place your entire foot at once, flat, on the icy ground. 
3) Furthermore, you do not want to separate your legs too far wide because this will lead to a slipping force on your back leg. 
So, having taken all these three points into account - what you need to do is place your foot flat on the ice without separating your legs too much. Which in other words means that you take small steps and walk like a penguin unless you want to risk a bad fall. 
