Using で or に in the sentence won't change the meaning. Both would be understood as Mike is excited because of winter vacation.
Both で and に can mean a reason or cause. The following is from the entry に. All the に used here can be replaced by で without changing the meaning (much).
6〔理由,原因〕for;with
恥ずかしさに赤面した
She blushed for shame.
うれしさに躍り上がった
He danced for [with] joy.
寒さに震えた
They shivered with cold.
彼らは飢えに苦しんでいた
They were suffering from hunger.
警報に驚いた
We were startled by the alarm.
On the other hand, 彼はがんで死んだ (He died of cancer., で is used for a cause) can't be ×彼はがんに死んだ. So it ultimately depends on the verb whether で/に is used.
BTW 私は学校でいます is not acceptable. It should be 私は学校にいます.