The Met Office warned the UK could be hit by the coldest January temperatures in 14 years on Tuesday night.
Snow-covered parts of Scotland could reach -15C overnight, said the forecaster.
Freezing temperatures and snow will continue for much of Britain this week due to a blast of cold Arctic air, before wet and windy weather sweeps in over the weekend.
More than 100 schools were closed in Scotland on Tuesday, while drivers faced difficult conditions thanks to the wintry weather across north-west England, including in Merseyside, Cheshire and Cumbria.
Yellow weather warnings for snow and ice are in place across Scotland, much of northern England and parts of North Wales until Thursday, then more mild temperatures are forecast along with wind and rain.
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.
Forecasters predict temperatures could plunge as low as minus 15C in places on Tuesday night.
In London, the temperature is set to remain around 2C throughout Tuesday night, though it will feel more like freezing.
More than 40cm of snow could be seen on high ground in north-west Scotland by the end of Friday as it continues to build up over the coming days, the Met Office added.
Meanwhile, lower ground in north-west Scotland could see between five and 10cm of snow by the end of the working week.
And while unlikely, there is a chance of a few centimetres of snow falling on the extreme south of England this week.
The Met Office is reviewing the situation and any new warnings could be issued at short notice, it said.
On Tuesday evening, the forecaster said in a post on X a weather system "skirting the south of the UK" overnight and on Wednesday could bring snow.
"This could bring a few snow flurries to the far south with a small chance of pushing slightly further north to bring more snow to southern counties," it said in a post.
There is a system skirting the south of the UK tonight and on Wednesday 👇
This could bring a few snow flurries to the far south with a small chance of pushing slightly further north to bring more snow to southern counties
Be sure to stay up to date with the latest forecast pic.twitter.com/PoxSo6rny9
— Met Office (@metoffice) January 16, 2024
The weekend is due to be milder across the UK, but westerly weather will bring wind and rain - and the potential for more weather warnings as the snow melts.
Stephen Dixon, spokesman for the Met Office, said: "We've seen a fair bit of snow already and more is expected in coastal areas, the north of Scotland, north-west England and south-west Scotland.
"It will be a continuing theme through much of this week."
He added: "Towards the weekend it's looking like we will return to a more western influence, so wet and windy as you get to Friday and it will bring temperatures up slightly.
"As you get towards Saturday you could see maximum temperatures of 11C in the south west of England which is much milder than what we've seen as of late.
"By Sunday we would see quite a deep area of low pressure moving in which will bring strong winds and heavy rain.
"The additional hazards will be snow melting and rainfall on Sunday."
The Government has confirmed thousands of households in England and Wales are eligible for cold weather payments.
They are made to vulnerable people, including pensioners, to help them pay for heating when the temperature dips below freezing.
The payments go to those living in an area where the average temperature is recorded as, or forecast to be, 0C or below over seven consecutive days.
Payments will be made to homes across Cumbria, Oxfordshire, Yorkshire, Northumberland, Norfolk, Staffordshire and Powys in Wales.
The UK Health Security Agency has issued a cold-health alert, which warns of possible impacts for the health and social care sector, while National Highways has put in place a severe weather alert for snow affecting north-west England 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."
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.
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."