This is from EB White's "Once More to the Lake" not charlottes web
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In this poem, White is writing from the perspective of a man who wishes to remember his youthful excursions and relive them with and through his son. The "old haunts" are the memories, the "chill of death" is the realization that time stops for no one. When he sees his own son struggling with cold swimming trunks, he experiences a "chill of death." This marked a moment where he came to understand lot only the loss of childhood, but the inevitability of death.
"Once More to the Lake"