Who said that you could not mix fire and water? Here is a perfectly good example: a half-water elemental red dragon. And while we're at it, we're giving it another head (the multiheaded template is my favorite). This allows us to make a cryo-based creature, which means it has the water, cold, and fire subtypes. Nothing says a creature cannot have both fire and cold subtypes (just look at Tiamat), though you may not want to make a practice of introducing such creatures into your campaign.