It might kill your enjoyment.
Unless you have skis with good edges, you will slide around a lot, and not in the ways you want to go...
It won't really do anything to the skis, per se. If they have metal edges they help you get a grip.
However, with a good pair of skating skis, icy just means fast and fun
Please, we need more snow, enough of this ice and rain stuff - ugh!