The southern ocean has clearly warmed. Satellite, ship, and buoy data all agree on this. Therefore, the growth of Antarctic sea ice is counter-intuitive, but there are several easy explanations (probably all working together).
Closure of the ozone hole has cooled the stratosphere, enhancing the cyclonic winds, which push apart sea ice, exposing open water which then freezes, increasing the volume of sea ice.
Increasing precipitation enhances a layer of cooler, fresher water that lessens upward transfer of heat from the deeper, warmer saltier water and reducing sea ice melting.
Now, let's discuss the Arctic...