The stranger came early in February, one wintry day, through a biting wind and a driving snow, the last snowfall of the year, over the down, walking from Bramblehurst railway station...
Hi could you help understand the meaning of the phrase "over the down" in this sentence please?

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New American Oxford Dictionary

down | daʊn |
noun (usually downs)
a gently rolling hill: the gentle green contours of the downs.