1. “寒假” 实际是个“假期”，是由多个holiday 构成的，应该使用复数holidays。

N-PLURAL （学校的）假期

The holidays are the time when children do not have to go to school.

...the first day of the school holidays. 

学校放假的第一天

2， 要么使用vacation（假期）。

3. “为我自己制定了假期计划”，应该说：make a holiday/vacation plan for myself。

翻译如下：

I am glad that the winter holidays are coming.  或：

I am glad about the coming winter vacation/holidays. 

I have made a holiday/vacation plan for myself。