A yellow warning is in place for snow and ice across Glasgow, much of Scotland, much of northern England and parts of north Wales until midnight on Tuesday.
The warnings continue across large swathes of the northern half of the country until Thursday.
Northern and eastern parts of Scotland saw the “bulk of the snow” on Monday, with 15cm on the ground at Aberdeen Airport by the evening.
A “cold plunge of Arctic air” has moved south across the whole country over the past few days, making it 5C to 6C lower than usual for this time of year, the Met Office said.
Met Office forecaster Craig Snell said Tuesday could see a “persistent band of snow” over three to six hours across Scotland, Northern Ireland and parts of northern England and Wales.
He said: “In the early hours of the morning we’re looking at temperatures getting down to -12C in a few spots, Tuesday night possibly down to -15C.
“So certainly a very cold spell into Wednesday.”
The UK Health Security Agency has issued a Cold-Health Alert, which warns of possible impacts for the health and social care sector.
National Highways has put in place a severe weather alert for snow affecting the North West on Tuesday, with road users advised to plan ahead and some rural communities warned they could be temporarily cut off.
Amy Fellows, national network manager at National Highways, said: “Freezing conditions bring so many hazards such as snow and ice, so take every possible step to understand your journey in advance and allow lots of extra time when travelling to prepare for the unexpected.”
Stein Connelly, head of transport resilience at Transport Scotland, said the cold snap had caused difficult driving conditions with further “severe impacts” anticipated on Tuesday.
National Rail has warned the wintry weather could affect train journeys all week with ScotRail saying services on the Highland Mainline route on Tuesday would be delayed by around 30 minutes.
Around 200 schools across Aberdeenshire, Moray and Shetland were closed due to snow on Monday.
Met Office chief meteorologist Andy Page said: “There will be widespread frost this week and we could see some fairly deep laying snow in parts of northern UK and strong winds could result in drifting or blizzard conditions at times.
“The snow and ice will be disruptive and could potentially impact travel plans, make driving dangerous and pavements slippery.”
