In episode 4 of season 8 there is a flash back scene were Wu meets Zane. Dr. Julian tells Wu that the master of ice visited them and that when he left Zane started acting strange.
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This means that Zane got his powers differently then the other ninja's. The other ninja's got there powers from there parents and Dr. Julian does not have powers.
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Zane got his powers from the master of ice. Here is a question for you, why would the master of ice have to give his powers to Zane? This is my answer. I think the master of ice is single and he was super old and ill so he had to pass on his powers another way. So he passed on his powers to Zane because he is brave and a good fit for master of ice.
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I think Zane gave his powers to Pixel. Zane still has his power but Pixel just has a little bit of Zane in her. In season 3 Zane gave pixel half his heart and Pixel could do spinjitzu with Zane. In season 8 pixel gets out of Zane's head and has her own body again. Pixel probably rebuilt herself and I think she has ice powers that she doesn't know about. So this is how I think Zane got his powers and how pixel got her powers, if she does have powers.