Personally, I believe that, as long as you make sure that your cat doesn't eat or bite the ice cube and doesn't get them often, it's fine. After all, my kittens hardly even lick the ice, as they prefer play. However, it is important to know what ice cubes alone, or in water, can do to your cat.
First of all, some cats actually try to eat ice cubes. Yes, you heard me, EAT. This can cause teeth problems, including broken and chipped teeth, which, in turn, can be the reason for trouble digesting, possible choking, and intense pain in the mouth. Not many cats actually do this, as more are inclined to lick ice, but it is recommended that you are alert when your cat is playing with or licking ice, or that you don't allow any ice on the floors at all.
Secondly, cats have very hot digestive systems and an equally steaming metabolism. Drinking excessively cold water on a regular basis or too much at a time can cause stomach discomfort and the metabolism as well as digestion to slow down. Even weight can be added on due to this. The best water to give a cat, many researchers say, is water at room temperature.
So, the verdict? Well, I will continue to let my cats play with ice cubes. However, I will monitor them closely and do it less often. I'll definitely not put anymore ice in any of my baby's water, even if Colleen gets a bit miffed that her princess treatment lost a perk. (She really shouldn't complain. She's so grouchy, now, that she won't even come inside!)
As for you, it's your decision. I highly approve of doing things to benefit and not harm your pet's health, whether your said animal is a cat, dog, snake, or tarantula. (I so want a tarantula!) Still, we must find a happy medium, as we can't protect them from everything. It's important to understand that people aren't the only ones with guilty pleasures, and while an overdose of something sweet can have negative consequences, we have to allow time and take time to appreciate those pleasures. Otherwise, life wouldn't be too much fun for anyone!