I have/had iron deficiency and was also anemic at times. I am lucky that I never was one to crave the ice. I do participate in an "anemia" board and, it seems, about half the people on there with iron deficiency anemia have the ice cravings and then the other half never do.
For those thinking about getting tests, a routine CBC will check for anemia but cannot really tell if you have an iron deficiency. You can have a severe iron deficiency but NOT be anemic (go figure) and you can crave ice with the iron deficiency without anemia.
The test you need to have done is "Ferritin". This test measures your iron scores. A "good" ferritin number is around 70. Mine was at "5" at its lowest point. My best friends was at 3 but she was not anemic. I've been told that anything under a 12 means you have no storage left. This will give you symptoms of fatigue, headaches, ice craving, etc, even if you don't have the full-blown anemia.
I think everyone likes to crunch on ice now and then, especially if it is a good, fine-chunk kind. But to want to do it all day should be a flag to get your labs done.