Well this is a question that only Game Freak can give a good answer too however I will use some mythology and links to perhaps make things a little clearer
dragons can easily be compared to the Greek gods of mythology as they were powerful beings that none could stand against, much like the Invincible Dragon types.
For Ice types I would put a link between Tartarus ( A cold, dark place) and Ice. Tartarus was according to myths the most feared place to be for both mortals and immortal beings. It was a deep, dark, icy-cold place where you could find no comfort. Using your hypothesis with the link of dragons and gods Tartarus is just the same thing for the Greek gods. Zeus himself didn't have much to say when it came to the Tartarus.
So just like the Tartarus was feared by even the gods, I would say that other then itself, the Dragon types only weakness was Ice (until gen VI). However not every type is hit supereffectively by Ice types. For this I would say since not all mortal beings have much to lose in the Tartarus, not all will equally be effected, whereas a God or Titian banished to the Tartarus will be rendered powerless (KO'd)
This explanation does sound weird, I know but it is merely just my Hypothesis