Most Preschools are private operations.
And yes, like companies, they usually get National holidays, off.
And they give the parents an annual calendar or schedule of when they are closed. So that the parents can find alternate care or backup care... ahead, of time.
Regular school is this way too, private or public school.
Per teacher in service day, this is typically when Teachers and the school do training or curriculum changes etc. If they do not have teacher in service days... then, the Teachers would need to come in on weekends to do it, off the clock. They would not get paid for it. Or they would have to get overtime pay for it etc. And that is not feasible.
Public and private schools/elementary, have those days too.
Often times, there are places that hold "intercession" programs for kids. Which is typically coordinated to most school's, holiday or non-school days. So look around in your community, for it. ie: the YMCA, or other venues that run intercession programs.
Schools, like other places of employment, have holidays. The workers are not year round workers. They get holidays too, and they often do not get paid holidays. So their paychecks are affected too. It depends on their employee, plans.
ASK your Preschool, for any Providers they know of, that DO do babysitting etc., for the days they have holidays and non-school days.
Preschools as a whole, does cost money. It is not cheap. And they are privately run, not government run nor are they public schools.