So what is the definition of ice. You're saying that it's blood, and that's what makes Jon ice and fire.

But if you're saying warging and skinchanging is ice, then Blackwoods are fair game, I would argue they have more old gods magic than the Starks do.

Also, I wouldn't discount d&ds interpretation of ice and fire. If they said so, it's because it's more likely than not that it was sanctioned by GRRM. People say it's fanfic, but game of thrones (tv show) is now canon. The cinematography defines Jon as ice, there's no indication he is fire at all. The fact that he is Rhaegar's son is not enough. His throwing a temper tantrum every now and then is not an indication of fire. Hell, who's to say that's not the wolf blood coming out? Brandon, Lyanna and Arya has it. He is defined in the text as most definitely Stark. It is repeated over and over in the books that he's got the Stark look.

Give me one scenario of Jon in the books and or show that displays his "fire" side. He's got no dragons, he doesn't look like a Targaryen, he's got a wolf, he's got the long Stark face, he's manning the wall at the north, what is fire in Jon?