BOSTON—A winter storm that had already blanketed parts of the South in snow moved into the Northeast on Friday, snarling air travel, crushing morning commutes and delivering a dilemma to school districts that had been trying to keep children in classes during a surge in COVID-19 cases. Schools in Boston closed, and Providence, Rhode Island, public schools switched to distance learning, but New York City kept the nation’s largest public school system open. “Children need to be in school. We don’t have any more days to waste” after the many closures and remote-learning days of the pandemic, said Mayor Eric Adams, a Democrat dealing with his first major storm after taking office Saturday. He also noted that many children rely on in-school meals and that some working parents can’t stay home. In central Pennsylvania, Ericka Weathers, a Penn State University education professor, scrambled to finish a fellowship application while her …