This winter’s uncommonly bad weather has offered a view into the de Blasio administration’s conception of the purpose of schools.

Asked why the city had decided to keep schools open today while also warning against unnecessary travel, Mayor Bill de Blasio and Chancellor Carmen Fariña offered a vision of schools as tools for social welfare. They also said that parents, whom they have said they want to involve heavily in the school system, should be free to decide whether to send their children to school on snowy days.

“I am a public school parent — I see these decisions through the eyes of parents,” de Blasio said during a press conference this afternoon, adding that while safety is “obviously first and foremost,” he was also concerned about unsettling families’ delicately made plans.

“A lot of parents have very difficult schedules and rely on the consistency of the school schedule for a good and safe place for their kids to be,” de Blasio said.

Chancellor Carmen Fariña reiterated that idea, noting that “no big businesses in the city closed so I’m assuming all parents who work had to go to work.” (She also noted that New York City has closed schools only about 10 times in the last half-century.)

Like de Blasio, Fariña emphasized that schools provide more than instruction for some students. “What about the kids for whom the schools is a safe haven?” she said. “Many of our kids would not have had a hot lunch today if the schools hadn’t been open.”

Their tone — which resembles the one they have taken when discussing the need to expand pre-kindergarten programs quickly — was very different from the one that former mayor Michael Bloomberg took when he justified keeping schools open in the face of bad weather. While he acknowledged parents’ logistical needs and said he aimed to make snow day calls the night before to help them plan, he focused on schools’ educational mission.

“There was no reason to close public schools today. What we’re trying to do is to get our kids an education that they’re going to need for the rest of their lives,” Bloomberg said in 2006 on a day when 62 percent of students made it through two feet of snow to get to school.

About the same proportion of students attended school today, Fariña said during the press conference. (Only 47 percent of students made it on another snowy — but sunny — day last month.) She emphasized that parents could choose whether to declare a personal snow day and keep their children home.

“The decisions parents have, not to send their kids to schools somewhere, is their decision,” she said.

The idea of parental choice made it into the city’s press release early this morning announcing that schools would be open but field trips canceled. “Parents, as always, should exercise their own judgment with regard to their children,” the release said.

The city’s press release announcing Monday as a school day did not include that line, but the one it issued last week did. On all three occasions, most districts near the city closed schools or opened them with a delay.

Fariña offered the same explanation a week ago at her first Panel for Educational Policy meeting. “You’re damned if you and you’re damned if you don’t,” she said in response to questions about how the city decides when to close schools for snow.

“Parents can make a decision about whether to send their kid to school or not,” Fariña said. “And there were enough kids in school today that for the parents who need the schools to be open, we did a great job.”