It is not illegal for schools not to have a holiday on New Year's Day. Because the task of students is to study, not to be laborers, the labor law is not applicable. Teachers belong to workers. According to the labor law, if they can't take a holiday, they should be given a series of holidays afterwards. But when the school is in winter and summer vacation, the teacher will also take a period of vacation, which is equivalent to a series of holidays. Therefore, it is not illegal for teachers not to have a holiday on New Year's Day.