The reason I say that I've been riding for 15 years is not to try to look like I'm a pro and I don't ever fall but to remind you that a few years back, there was no such thing as a snowboard helmet and nothing serious never happened to me or my riding buddies or to friends of my friends. I'm not saying that there is 0% chance of head injury, accidents do happen ( and chances are I'm going to get a helmet for icy days)but I don't think it's absolutely essential. Maybe I'm wrong...but it really is the OP's decision at the end.
For just ice? Riding powder they are actually pretty good to have. I ride a ton of powder and you just never know where a hidden rock is going to be if you take a tumble. Then again, you can say that about any of the conditions, there is always that "if". As you said it is personal preference with the OP. Helmets are never a "bad idea".