Ice was a biggie for me too. I would go by the shaved ice stand and get like 5 cups at a time "no syrup please". The lady would just laugh..... I'd take each cup as it was handed to me and dump it in a 2 quart cooler. Finally, one day she said "Why don't you just give me the cooler and I'll fill it up"
There is acutally a disorder in pregnancy called PICA. It is where you eat ice or frost. (first named back when freezers weren't frost free). It can also be where you eat starch.
If I remember right, as long as you don't take it to extreme and eat healthy otherwise, it is ok. However, if you eat TOO much ice, it can make you anemic.
I would suggest you do share this craving with your Dr, so they can keep an eye on your bloodcount.