Sub-Zero as well as the rest of the Lin Kuei, I believe, was originally meant to be pure Chinese....despite the fact in MK1 and 2 he's played by Daniel Pesina who was clearly not Chinese.
I guess his MK2 ending was an attempt to follow through on that, but was dropped in MK3 when John Turk began playing Sub-Zero.

It was then explained in MK: Mythologies that Sub-Zero is half Chinese and half American...stating his father was a Chinese Lin Kuei warrior who married an American woman.
Thus explaining Sub-Zero's caucasion appearence.

This all became moot when they revealed Cyrax was black....but nevertheless, he was supposed to be Chinese, but he was always played by non-Chinese actors so they incorporated it into the story.

IMO, he looks the same in Deception, so I don't know what you mean by he went back to being Chinese.

Sub-Zero was originally going to be Chinese, but due to the actor who played as him in MK3-MKT, they gave him and his brother an American heritage for his background story in MKM: SZ. I think it's more so that they are part Chinese. For MKD, they wanted to give his alternate costume look, particularly the hairstyle, a Chinese feel to it though that doesn't change his American roots.

So to sum it up, he's a Chinese American who is a descendant of the cryomancers on his father's side.

ohhhhhhhhhh

Chinese Ninja Warrior

With your heart SOOOOO cold

Sub Zee-herooooooooooooo

Xiahou and Sub prety much covered your question.