Ok.  That works.  I always considered Ice to be separate, the way lightning is separate from fire and metal is separate from Earth.  I guess that since every water bender can do it, though, it might as well not be.

Edit: Saw she had the habit of swearing. Note to self: use the phrase "by Vaatu" (basically "hell" in modern language) when talking to you at some point, possibly to get you to stop humming.