As Dave mentioned, suspended skin might require caution and good judgement (why would anybody with good judgement be paddling through ice in the first place???
) On a typical wood/canvas you might scratch the paint, but that's about all. Plastic, fiberglass, etc. might be better if you're worried about damage.
Someday, somewhere, before you hang up your paddle for good, find a lake with about 1/4" of nice black ice on it and a nice sunny day without wind. Take a long, strurdy paddle that you don't mind abusing a bit, kneel in the canoe and make a 3'-4' wide path through the ice as you paddle. You do part of this by sliding the bow up onto the ice a bit and letting it break the ice as it settles down and part by chopping with the paddle blade. Go for a while and then turn around (make a loop) and follow the path back.
Why? You ask? First of all, it satisfies some childish desire that most of us have to break things - like popping bubble wrap. Secondly, on a still, quiet day the sounds are priceless! All the little broken bits along the edges of your path move with your wake against the ice sheet and sound like the ice cubes rattling in a thousand scotches on the rocks. With every paddle stroke, your return trip sounds like wind chimes. Absolutely worth the price of admission and one of those simple paddling experiences that you remember for years.