has the same structure as = _before Hanako reaches the school_. Thus it means _before the color of snow goes that far_.
I think it is a matter of interpretation, but the part resonates with the beginning
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So it is late in the evening, and the scenery Shimamura is seeing is colored white at bottom. He sees barracks in the distance, but the color of snow is already gone around/before there. (This may sound not logical, but I don't think it's surprising in Kawabata's writings.)
* * *
The translator takes the subject of '' as the barracks. I'd say it is possible, but then it would be definitely more natural to say **** .