In a letter to parents sent on Wednesday evening, headteacher Louise Newport said she had contacted various agencies about clearing roads and pavements surrounding the school, but without success.
She added: “We have had a small amount of the school driveway cleared but due to the thick ice underneath the snow, after five hours of hard work the contractors have had to stop. They were unable to clear any of the snow and ice from the roads.
“The ice is making driving and walking near school impossible and very dangerous.
“I have been on site this afternoon to assess the risk further but after a tricky and long walk from the leisure centre to school it would be impossible to open the school without putting everyone at risk.”
The head said the situation was complicated further by the restricted access to the school site for emergency vehicles.
She added: “This risk is too high, therefore, to keep everyone safe, we have no option but to close the school tomorrow.
“I understand that this is difficult for everyone, and we all want school to re-open.
“However, my role as headteacher is to ensure everyone’s safety and not put anyone at unnecessary risk.”
A number of parents on social media have blamed North Yorkshire Council for failing to help, while others have suggested military personnel be deployed to assist the school.
North Yorkshire councillor for the area, Kevin Foster, said he had made “strong representations” to his authority’s highways department to help the school.
He added: “It’s a really difficult situation and I don’t know what the answer is.
“The council has 5,800 miles of roads to deal with and it’s how you prioritise the worst areas.
“I just wish I had a magic wand to get rid of all the snow. My phone has been red hot for days with people in need of help.”
A Ministry of Defence spokesperson said: “Whilst we have not received any official requests from the civilian authorities to provide assistance, we stand ready to support the local community should the need arise.”