Fairfax County’s unprecedented decision to cancel classes because of frigid temperatures Tuesday was partly out of concern for students who walk to school and for those whose parents might not be able to afford clothing that would be appropriate for extreme cold, school officials said.

“When you have a large high-poverty community, you need to be thinking about those students and if they own coats,” Fairfax County School Board member Ryan McElveen (At Large) said, referring to the system’s 47,000 students who qualify for free or reduced-price meals, a federal measure of poverty. “That played a role in the decision.”

With temperatures forecast to be in the teens early Wednesday, Fairfax County again plans to alter its schedule with a two-hour delay.

Loudoun and Prince William counties also closed schools Tuesday, citing concerns about student safety, especially for the tens of thousands of students who walk to school and would have faced near-zero temperatures. But other school districts in the Washington region had different responses to the cold snap, with some opening as usual and others delaying their start by two hours.

The varied decisions meant that some area students stayed at home while others just miles away waited at bus stops or walked to school in the bitter cold, stirring discussion among parents about when schools should close, especially if there is no precipitation. Some parents questioned the rationale of delaying the start of school for two hours, as temperatures held in the single digits — before factoring in wind chills — throughout the morning.

Schools in Prince George’s and Arlington counties and Alexandria opened two hours late. Kelly Alexander, a spokeswoman for the Alexandria school system, said officials thought the “delay would give us a little time to warm up.” She said the extra time allowed officials to ensure that schools and buses were warm.

Schools in the District and Montgomery County opened at regular times, but two District schools — Anacostia High and Hardy Middle — had weather-related problems overnight and had to cancel classes. Four schools in Montgomery closed early Tuesday because of problems with power, heat and water.

A fire alarm went off at Winston Churchill High School in Potomac, apparently because of a malfunctioning water pipe. Students were sent outdoors for 10 minutes, schools officials said. Some were without coats as they waited for the building to be deemed safe.

Montgomery schools spokesman Dana Tofig said safety is the decisive factor in making determinations about school closings.

“Everything is taken into account when we look at whether to stay open, or to close, or to delay,” Tofig said, noting that many children in Montgomery rely on the school system for two meals a day, under the free and reduced-price meals program. “Different districts make different decisions . . . and we believe we made the right decision to have school today and provide education to 151,000 students.”

Prince William County schools officials made the decision early Monday afternoon to cancel school Tuesday, so they could begin informing parents by the end of the day. They decided that the cold was too much of a risk to children who walk to school.

“The combination of a forecast of record-breaking cold and unprecedented wind chills led to the possibility of danger, especially for the more than 20,000 walkers we have,” said Phil Kavits, a schools spokesman. “Really, the conditions made for a fairly easy call, because we don’t want to expose students to these kinds of dangers associated with this kind of cold.”

In Loudoun County, classes were canceled for the second day in a row. On Monday, officials were mostly concerned about icy road conditions. By Tuesday, they were worried about the temperature.

“This is record cold. You just don’t want children exposed to it,” said spokesman Wayde Byard.

Some parents in the District — where schools had been closed for winter break since Dec. 20 — were thrilled that vacation was over, especially after closures in December for snowstorms that never materialized.

“We are desperate to get these kids out of this house,” said Capitol Hill resident Tim Krepp, only half-joking. The Krepps normally walk or bike with their two children to Brent Elementary, 18 blocks away. But Tuesday they broke with routine and drove.

Other parents argued that it was too cold for children — especially those whose parents can’t or don’t drive — to make their way to school. Unlike suburban school systems, the District does not provide school buses except for students with disabilities. Some students use public transit, while many others, especially elementary school students, walk.

“I’m very upset because they can see it’s 7 degrees outside,” said Tracie Smith of Southeast Washington, who said she was keeping her fifth-grader home from Patterson Elementary.

The school system opened its buildings 45 minutes early so students wouldn’t have to wait outside. But Smith worried that wouldn’t be early enough for many children, who leave home when their parents go to work. “A lot of kids don’t even have coats,” she said. “The wind is so cutting, it is painful for adults. A child is going to be an icicle.”

Trayon White, who represents Ward 8 on the D.C. State Board of Education, said he had heard from many concerned parents. “This is ridiculous,” White said. “It’s too cold.”

Rockville parent Robbin Brinkhoff applauded Montgomery’s decision to stay open. “I think we’ve become a little too pampered and lax,” Brinkhoff said. “This isn’t the worst that is out there.”

She offered rides to a couple of children who she thought might need them.

Prince George’s officials said they decided on a two-hour delay to give maintenance workers enough time to resolve any problems that arose because of the weather.

As Ashanti Foster, a mother of six in Mitchellville, dropped her children off at Lake Arbor Elementary School, she said that on one hand she questioned the rationale of opening school. On the other, she said, schools are a “safe haven,” a place where many low-income students have heat and a warm meal.

Emma Brown, Michael Alison Chandler and Donna St. George contributed to this report.