回答
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I feel even more like winter has come.
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It increases my feeling that winter is here.
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It gives me even more of a wintery feeling.
wintery = 冬っぽい、
wintery feeling = 「冬だ!」っていう感じ
回答
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to feel (even / a lot) more like winter
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to feel as though winter has truly come
「より一層冬がきたことを実感する」は直接に英訳したら、あおいさんの言いたいことがちゃんと通じますけど、この言い方はよく聞いていないと思います。
"It feels even more like winter."
"I feel as though winter has truly come."
わたしだったら、"Now it feels like winter" と言います。