I know this is a different situation than the OP described, where the rear went out from under him, but I wanted to mention this also.
I'm running Duratrac's and I was driving around in the snow we just had yesterday here on the East Coast. I noticed that when the front tires tried to skid forward as I turned into a corner, I just had to give it a little gas and the front tires grabbed again and pulled me through the corner. That's completely non-intuitive, but in an AWD like the LC's, it's very effective. I did this multiple times to test the truck, and I got the same result each time. Worth taking the time to show this to the kids and wife as you give parking lot instruction.
That may work on snow but not so sure about an ice patch. Although I've never driven on the east coast in snow. In tahoe area things tend to melt during the day and freeze at night causing ice patches inbetween and under snowcover. Acceleration could send you off a cliff.