Wasn't there a disagreement between the Governor of New York and the cities of New York over when to close the schools? If I recall correctly the cities wanted to close them earlier.
Also was the subways ever shut down in New York City?
Closing the subway isn't feasible or practical. A lot of essential workers rely on public transportation. They have to protect themselves while commuting. So no, the subways there and same here in DC are still running, although more limited than before.