My Dr. said craving ice is a sign your iron is low and that actually eating ice lowers your iron (I'm not sure how that works, but that's what she said). You definitely need to mention your craving to your doc. You need your iron to be built up before you have LO. Plus, getting your iron up (assuming it is low) will help you not feel so fatigued.
The only time I chew ice like a fiend is about half way through my pregnancies, which is also about the time I was diagnosed with low iron (both pregnancies). I've heard they are correlated and they seemed to be for me. Definitely ask your doctor to check your iron. It drives DH crazy, but it's like an obsession for me when I'm pregnant.
Although chewing ice is a sign of low iron some people just chew ice. I know I have always been borderline anemic and have always chewed ice. But I actually enjoy it. Its not something I crave but its such a nice way to stay cool when I feel warm and I do not like drinking tons of water so at least I am getting it that way. I think it depends on if this is something really new ( which is sounds like) so like PP said I would definately mention it to your doctor.
Yes, definitely a sign of anemia. If it helps, I was not anemic the entire pregnancy until 2 weeks ago when my hemoglobin dropped pretty significantly. Thought it would have happened earlier. Hope it works out for you.
Re: Chewing ice
Yes Ice and cold water. I figure its my sinus infection and soar throat.