When we walk on ground, we apply a force on the ground obliquely. The friction part of the reaction force from the ground on you, will prevent you from slipping. On a frictionless surface, as there is no friction to oppose you, you may slip and fall. However, Newton's third lay says that if you exert a force on an object, that object will exert an equal and opposite force on you. Here, wont the law break, as there is no force that is exerted by the floor, in reaction to the force applied by you on the floor ?
Newton's third law still holds. You cannot apply a friction force on a frictionless floor, and it cannot apply a reaction to that friction force. No matter how hard you try, you will simply find that no force is applied.
You and a frictionless floor can still exert other forces on each other, like the normal force that supports your weight.
You aren't applying any horizontal force on the floor. That is why you slip and fall on the spot - you aren't moving forwards. So there is no violation of Newton's 3rd law.
Just think of punching into a wall and then into thin air. In the latter case you aren't exerting any force at all on anything even though the act seems to be the same.
You are still applying a vertical force on the floor, though. And in respons the floor exerts a normal force upwards. Again, all is in order with Newton's 3rd law.