Still havent gotten skis yet, but I have a question.

The trail near my house is rutted and icy. They do not groom it.
Lots of foot prints and ruts and ice, some snow left.

Will icy conditions kill XC skis?

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!