We would say (わたしは)　冬が待ちきれない　／　ふゆがまちきれない You would hear these expression in daily conversation: クリスマスが　待ちきれないよ 夏休み(なつやすみ)が待ちきれない 週末(しゅうまつ)が待ちきれない All of them expresses that you are so excited that you can't wait for it. You are very looking for ward to it coming up.

私は冬を待てない／わたしはふゆをまてない I'm not native and this is pretty literal, perhaps someone can give some other options.