What is the effect of ice on concrete?

So long as the concrete is fully cured, ice won't hurt it in your lifetime.

If it's not fully set, you'll need to keep it covered with an insulating blanket until all the water has evaporated and it looks dry (light gray}
Concrete generates heat as it cures so all you'll need is a blanket this time of year.
If it gets down into the teens, you'll need to put additives in the concrete and add a heat source to aid in the curing.