介词与 holiday 的搭配是这样的：

on holiday（不加冠词和其他限定词my等，指 “度假；在假期期间”）

during one's holiday（具体到某人的假期，指一个时间段。）

A (或one's) holiday is a period of time during which you relax and enjoy yourself away from home. People sometimes refer to their holiday as their holidays. (外出度过的) 假期 [英国英语]
例：
During his summer holiday he visited Russia.
暑假期间他游览了俄罗斯。

此句不用 on, 因为不是某一天，而是一个时间段（暑假期间），所以用during。

由此得出：my holiday 不是指 “一天假期”，而是指一个时间段，所以不用 on, 而用 during。