Yes, the classic game can be played on ice. Thanks to the folks at Wise Geek, you too can make your own table hockey ice rink. I really like the mini Zamboni they have there. Nice touch!
This reminds me of a time my buddy and I played a memorable best-of-5 series at ESPN Zone in New York City. It was absolutely brutal and both of us left exhausted, blistered, bruised, and bloodied (We play a real no-holds barred style). I can only imagine the damage that would have occur if the puck was flying even faster on a small sheet of ice. Brutal!