I think that is should be It had been snowing all night because this is something that happened in the past. Since you're referring to yesterday. "Was snowing" refers to the present, not the past like you're trying to do.
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hrsaneiWhen I woke up this morning, the world looked magical. It was snowing all night.This is one of those cases that sounds correct as long as you don't stop and think about it very long. Personally, I consider it less than careful. We native speakers are likely to accept it as an adequate substitute for the more logical, I think,