I'm not sure that I would use ice though. It seems like some parts of the cutting may actually get frost bite if they come in contact with the ice for too long. My refrigerator is colder in one spot in the back, and I assume this is not uncommon. My fridge is set pretty cold and will slightly freeze liquid if I keep it in that cold spot. I would just put the cuttings near there, and they should stay pretty much the same as if you put ice in with the cuttings. If stuff doesn't freeze in the cold spot, I would put the cuttings there.

But hey, I've never tried it. If you're sure the ice isn't damaging the plant at all, don't fix it if it aint broke.