Since you are part time you will have to take unpaid time off, or so I imagine.
My recommendation is that you have this discussion as soon as possible. I would be completely honest and describe what you did here.
For them to ask this early about December 23rd, tells me that they already like you and are planning on having you around.
I had a very similar situation when I took my first job, but that was 26 years ago. I had a family reunion in Germany in October and I started the new job in September. I told them before I started that this important family trip had been planned for some time, and would it possible for me to still attend. They made it work out. But manufacturing was slow that month.
Since you do have some degree of flexibility with going in the summer, and it's only 6 months away, and you might even enjoy the weather more..there is a good chance arrangements can be made now.
GL!