Can't think of any. It will make the area go numb and she might not like it. So, only do what she thinks is fun or feels good.
This is actually a thing, and no, I can't see how it would affect anyone unless the ice was too cold and caused an ice burn, which is very possible. The way to do this more safely is to put the ice cubes in water and apply the cold water. I'm a guy and I've done it, and it makes the nipples very sensitive to touch, if one likes that. For some, it might make them too sensitive which would hurt. It's really nice in hot humid weather because sweat can make skin not sensitive to touch for those who have discovered the erotic nature of touch. Keep in mind that not everyone has and not everyone wants to.