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

$\mathrm{f}=\mathrm{\mu }\times \mathrm{N}$

Frictional force depends on coefficient of friction (roughness of surface) and the normal force (in case of ice the coefficient of friction is very small and it is independent of the normal force so independent of step size )

$\mathrm{f}\propto \mathrm{N}$

Case when u keep longer steps the angle of inclination of leg with vertical decreases and hence normal force decreases and so does the friction.

Case when u keep smaller steps the angle of inclination of leg with vertical increases and hence normal force increases and so does the friction.
so, smaller steps is taken to make sure the friction is larger