To avoid slippping while walking on ice, one should take smaller steps because of the 

In the diagram shown, P is the force applied by the man on the ground and $\mathrm{Psin}\mathrm{\theta }$ is the horizontal component of this force. As shown in the diagram, for smaller steps, $\mathrm{\theta }$ is small, so smaller frictional force (f) can balance $\mathrm{Psin}\mathrm{\theta }$.