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).
She blushed for shame.
He danced for [with] joy.
They shivered with cold.
They were suffering from hunger.
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.