Most Element/Energy powers tend to deal with things that are not physical as such (such as fire, infernal or radiant) while Material deals more with physical substances, such as stone, metal and plants. Basically if you can hold it in your hands normally, then it is more likely a Material rather than Element/Energy. That said, there does seem to be overlap between the two categories... with Cold including things like Ice and Weather creating rain and such.
I was actually thinking of a character more like Aquamaria or Hydroman that are both made of "living" water as well as being able to control water... basically a Water Elemental of sorts, when I noticed there wasn't any power that actually controlled water as such.
As for using both Fire and Cold to represent water... it seems rather inefficient to use two powers to represent one, especially when one of those powers is often seen as the opposite of the power you are going for.