Some players with perfect form and balance can throw with power and control on a sheet of ice (Al Schack and Joe Giebel). The rest of us tend to slip, slide and occasionally face plant. As a forehander who throws bent over and low to the ground, I have almost perfected the face plant. The key is once you realize your plant foot is slipping out don't fight it, just tuck your shoulder into a barrel roll. This saves the shot and most of your skin.
But, of course the better solution is to somehow keep grip on your plant foot and stay on your feet.
The best solution I have found is sheet metal screws. Drill them into the bottoms of your boots.
I use the half inch screws and a power drill. You can install them in minutes. We have been using them in Michigan for many seasons and they are now common amongst experienced tournament players. The screws will eventually fall out or wear out so they need to be replaced periodically.
The greatest advantage is that you can take most shots and be confident about your footing.