It isdifficult to walk on slippery road because the friction is less and the required grip is not available.
By Newton's third law: you push backward with your feet,the ground pushes you forward. But that interaction is friction. Reduce friction and it doesn't matter how strong your legs are, the surface is incapable of pushing you accordingly. The coefficient of static friction is very low so it is easy to slide your foot rather than push. Accordingly, the ground doesn't push back.