Teachers are having to open windows as a Covid precaution, despite temperatures plummeting as pupils returned to school this week.
The National Education Union (NEU) has demanded the government invest in more air purifying units, which improve indoor ventilation and are a warmer alternative to opening windows.
The devices were trialled in primary schools in Bradford before Christmas to see how effective they were.
The Department of Education announced the purchase of 7,000 purifiers this week, saying they were only needed in a handful of classrooms as a "quick fix", where opening windows was impossible.
But the NEU's Wakefield district branch secretary, Sally Kincaid, said they should be rolled out to more schools, beyond what she described as the "miniscule" numbers covered so far.
She said: "It isn’t just our members who are freezing cold, it’s the kids as well, who are having to sit in classrooms with woolly hats and gloves.
"It's especially bad for older primary school children who are sat down for most of the day and can’t move about.
"These purifiers have been used in places such as New York and Hong Kong and they work."
"They cost about £200 each. That's a lot for schools when they're budgets are so tight at the moment.
"But for the government, buying one for every classroom would cost them about half as much as the Royal Yacht."
Mrs Kincaid said local teachers were reporting very high readings on carbon dioxide monitors they've been using to measure ventilation, which demonstrated how badly the purifiers were needed.
She added: "We want our children in the classroom and we want schools to be open.
"But if we’re going to avoid the chaos we’ve had previously, with pupils being off and schools being short of staff, something has to be done."
Speaking earlier this week, Education Secretary Nadhim Zahawi said: "There is no doubt that the Omicron variant presents challenges but the entire education sector has responded with a Herculean effort, and for that I thank each and every one of you.
"The Prime Minister and I have been clear that education is our number one priority. These measures will bolster our support schools as we do everything in our power to minimise disruption."
Local Democracy Reporting Service