What is a limited slip differential?
Getting back to the situation in which one drive wheel is on the ice and the other one has good traction: With this limited slip differential, even though the wheel on the ice is not able to transmit much torque to the ground, the other wheel will still get the torque it needs to move. The torque supplied to the wheel not on the ice is equal to the amount of torque it takes to overpower the clutches.