Forecasters have warned there is no sign of a let-up in the icy conditions, with several more centimetres of snow continuing to fall in the North East and parts of eastern Scotland over the coming days.
The rest of the UK will also be affected, with snow moving south, and only parts of western Scotland and Northern Ireland will be free of snow showers by Tuesday afternoon, forecasters said.
In Scotland, more than 600 people were offered emergency accommodation at a sports hall in Perth after they were stranded overnight on Sunday on the A90, M90 and A9 amid blizzard conditions.
All schools in Dundee, West Lothian and Shetland are closed on Monday. Across York and North Yorkshire, around 50 schools were forced to shut, with several schools in East Yorkshire also closed for the day.
The coldest place overnight in the UK was Altnaharra in northern Scotland, which recorded a low of minus 16.1C.
Llysdinam, which saw Wales's chilliest November reading on Sunday at minus 18C, was a bit warmer on Monday at minus 12.9C.
Forecasters warned that the rest of the country is likely to be blanketed this week. The severe conditions could also last well into next week, with rain, sleet and snow.
Brendan Jones, senior forecaster with MeteoGroup, said snow would be moving south across the UK with many areas starting on Tuesday morning with a covering of snow.
"We now have snow showers further south, parts of East Anglia, even down into Kent are seeing snow showers at present, even into the East Midlands," he said.
"The snow shower risk is expanding further south and a little bit further west as well but not getting into Wales at the moment. The only exception is the far south-west tip of Cornwall which is seeing some hail and snow. "
The AA said there had been "unprecedented" demand for its services compared to a normal Monday in November, with around 12,400 calls for assistance, coming in at more than 2,100 every hour.
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