No. Working as a student is not at all connected to the season. You choose when you work and for how long.
Do you want to sell ice cream for 600 hours in summer? You can. Would you like to keep a few hours aside to work as Father Christmas later in the year? No problem.
Whatever you do, just make sure that you:
- stay within your quota and,
- go to your classes or other school activities (you may not work as a student during class hours).