I don't think it will do them much harm, to be honest I have never noticed them get irritated when drinking water, ours is straight from the tap, mind you it is often sitting for almost 24 hrs before they drink it anyhow, I am only passing on what I read on the Whiskas site, which is a good site with lots of helpful information, so I think it is pretty reliable.

I am curious, do cats like their water really cold , like out of the fridge or just cool, just a thought?