There are no holidays in the unemployment benefit system. On the other hand this means that, If a national holiday falls on a weekday (mon-fri), you must be available for the labor market. This also applies when Christmas Day fall on a monday like this year.
Obviously no one from the Jobcenter or you A-kasse will call you in for a meeting or jobinterview on a national holiday - but you must search job according to what your A-kasse has told you is the minimum number of jobs you must apply for every week (if they have told you that). And you must also update your job log at Jobnet.dk during national holidays - as if it was a normal period with dagpenge/unemployment benefits.
If you do this, you will get paid for national holidays. You get paid for 160.33 hours every month, regardless of how many national holidays there are in the month.
To be available to the labor market, you must also stay in Denmark. This means that if you go on a holiday trip on Christmas days, you will not be able to receive unemployment benefits for the days you stay outside Denmark.
Instead, if you plan to go on holiday - outside of Denmark - you can apply for holiday unemployment benefits ("feriedagpenge") in your A-kasse, or if you have earned right to have holiday from previous job, you can off course use your earned holiday money ("feriepenge").
You must always notify your JobCenter and your A-kasse of any holiday plans no later than 14 days before the first day of the holiday.
If you stay in Denmark during the Christmas you dont need to inform anybody - and as mentioned you will receive dagpenge for the hole december (160.33 hours) like other months.