1.我們也放寒假了
We are also in our winter vacation.
Our winter vacation also begins.
2.寒假期間你有打算做什麼嗎 ?
Do you plan to do anything during the winter vacation?
Do you have any plan for the winter vacation?
What is your plan for the winter vacation?
Unless I don't understand properly, "寒假" shall be for students and teachers only. However, "summer or winter vacation" is NOT specifically for students and teachers only.
2014-01-19 23:14:13 補充:
To translate "寒假", I suggest to use "winter break" or "between semesters for the fall (semester)".