With the transmission in “Park” and the emergency/hand brake not on, only the input to the rear differential will be locked. Now if either one of the rear wheels looses grip on the ice, what you would see is that it would in fact start to turn in the opposite direction to what you would expect. It would be being driven by the gripping wheel on the other side which is now free to rotate as the vehicle moves forward.
This would be the same effect if you jacked both rear wheels off the ground while in “Park” and turned one of the wheels by hand. The other wheel is still able to rotate in the opposite direction. The wheels are not locked, only the differential input is locked.
You should have applied the emergency/hand brake. Braking then acts individually on both wheels. One wheel loosing grip would not affect the other wheels braking ability.