There are a lot of Roman Catholics in Madison, so one of the holidays being celebrated yesterday was probably the Feast Day of St. Frances Xavier Cabrini. Mother Cabrini was a nun who founded the Missionary Sisters of the Sacred Heart, a Catholic religious institute that gave aid to Italian immigrants in the United States, and who was the first citizen of the United States to be canonized by the Roman Catholic Church. I would've thought it more likely for the library to clase for the Feast Day of St. Jerome or St. Catherine of Alexandria, both considered patron saints of libraries and librarians, but what do I know.
This part of Wisconsin has a fairly substantial Hmong population, so I think it's likely that another of the holidays being observed by the MPL yesterday was Armed Forces Day in Vietnam. What better way to reach out to the Hmong people than by honoring the organization that caused so many of them to flee to the US to avoid being killed?
Thirdly, Dec. 22 is National Mathematics Day in India. With UW-Madison having so many Indian students, many of whom are here to study math or other subjects that require math, like science, technology, or engineering, closing in observance of that holiday would be a logical way to pay tribute to that portion of the local population.
Another possibility is that they closed for some other reason, and only claimed that it had something to do with the holidays. I don't know why they'd lie, though, so I think my guesses are more likely.