I would assume this is to add ambience and mystery to the setting, that, and Foster says weather is symbolism. She's probably using the dreary, cold frost of winter to show the dull coldness of her childhood.
I think the author put it in the winter because it's a sad time for Jane. She has to live with her aunt and cousins who abuse her. It wouldn't make sense for the author to put it in the summer time because Jane is not happy. Nor or put it in the spring because she is not having a new beginning. SO that's why I think the author put it in the winter.
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