When I was driving taxi (somebody else's car) and was on ice I tried it, the transmission does go into reverse. Putting it into park didn't happen, I guess the gears were turning too fast. I did hear something rattling until I dropped down to about 5 mph, then it dropped in and locked the back wheels, which was a non-event, being on ice.

Putting it in reverse and punching it on ice turned out to be a much better way of stopping than using the brakes