You could also replace it with "the mentioned dates" or "the aforementioned dates". But I'd still go with "they" unless there's some other reason not to.
Am I the only person who would use "or" between the dates? I would use one of the following:
There will be no class on December 25th or January 1st because they are bank holidays.
There will be no classes on December 25th or January 1st because they are bank holidays.