Some principals doubt they can adequately ventilate their classrooms to reduce the spread of Covid-19 during winter.
They say leaving doors and windows open is not practical on cold days and the 5000 air purifiers the Education Ministry is providing will not be enough for the country's 2400 schools.
They say their best hope of containing the virus will be continued use of face masks, and a drop in the number of community cases.
The Education Ministry has told schools it is testing the best ways of maintaining good air flow during winter.
In the meantime, it is telling them to heat rooms on cold days before children arrive for the day, and then leave doors and windows partially open.
Port Chalmers School principal Vicki Nicolson said it would try that approach and use a ministry-provided CO2 monitor to see how effective it was.
"It seems a bit silly to light a coal boiler or heat classrooms if we're then opening all the windows so what we're going to do is light our boiler or heat the rooms, keep the windows and doors shut at that point, and then about 8.30 once kids start arriving we'll open the doors and windows," she said.
Nicolson said she did not yet know if the school would need an air purifier, but if it did she doubted that one would be sufficient.
"Until we do start putting heaters on, until we do start closing windows and doors, we don't know what that's going to do to ventilation in classrooms so those CO2 monitors are going to be great. But you know, if you've got three or four classrooms that need ventilating and need to be air purified, one [purifier] is only going to affect one space," she said.
The principal of Mamaku School near Rotorua, Gary Veysi, said opening doors and windows was not an option on the coldest days at his school.
He said he was expecting one air purifier from the ministry, but it would not be enough.
"Realistically, if we get one for the whole school, what's the point? Do I pass them around to each teacher for half-an-hour a day?
"My concern is, come winter, when it's cold, we can't have the windows and doors open up at Mamaku. Sometimes it snows, so if it's snowing the weather's bad, we can't afford to have the windows open or have the heat pumps running at full capacity just to try to keep the heat," he said.
Veysi said the school would have to find other ways to cope, because testing showed CO2 levels exceed the recommended ceiling of 800 parts per million when windows and doors were closed.
"They really creep up quite dramatically so how can we have breaks in the day, so we might go over to the hall ... open all the windows and doors let that fresh air come through, then come back and close up again. So it's just managing the day," he said.
The principal of Freyberg High School in Palmerston North, Peter Brooks, said he doubted the school could meet the ministry's ventilation guidelines during winter.
"You obviously can't get air purifiers suddenly put into 80 classrooms, they're not going to be providing schools like us let alone over the whole country so yes, I'm very much watching this space on how we're going to do that," he said.
"I guess I'm hoping like everyone else that we've got through the worst wave of Omicron and not too bad a second wave. To be blunt we're really going to be relying on mask-wearing."
Brooks said the ministry's recommended approach of leaving doors and windows open was not practical for many secondary classrooms because some, such as science labs, could not be left open and unattended.
The Ministry of Education said it had ordered 5000 air purifiers and by late last week it had sent 300 units to 250 schools.
"These have either been sent to schools as a temporary solution while longer-term property interventions are underway or as the first part of our general distribution to all state and state-integrated schools through to May."
It said the purifiers were being sent first to schools in areas with low vaccination rates and deciles, and those in highly variable or cold climate areas.
The ministry said most spaces in schools were well ventilated and so far 50 schools had asked for help with air quality and 12 of those had been sent air purifiers.
The circumstances around the death are being treated as unexplained.