Yes trains even operate on Holidays I recommend to use websites like bahn.de and Intercity.pl to find your timetable. 
As there is the anual timetable change before many websites have just their own timetables and not foreign ones. 

E.g. bahn.de that usually provides a good planning option for International journeys still doesnt have all timetables loaded.
Netherlands - Berlin - Poland if you provide more details it would be even possible to show an example

You need to do the work youself and check the time table for the train you want to take. A good place to check is Bahn.com

Warning-hopefully not in force anymore, but chance s it still will be:

just east of Hannover on the main hi-speed line from there to Berlin-which you obviously have to pass then- was a recent train crash and the line was blocked and partly destroyed. It still is, of course they are working on it-but the previous date of repairs was not met.

Only on that funny island on the NorthSea do they stop all transport on 25/12.

To catch out however- what may do not realise, is that on the morning of 1/5-the day of the red flag waving jolly workers-in many countries all local transit is stopped to give them the chance to do just that (does not often apply to trains though)