A vehicle negotiates heavy snow in Duston, Northamptonshire
The coldest snap for 20 years shows no sign of letting up, with the freezing weather expected to last all weekend and into next week.
Almost anywhere in the UK can expect a further covering of snow on Sunday and Monday, the BBC Weather Centre said.
It comes as driving groups warn ice is making roads extremely dangerous.
Councils are running low on road salt and Gloucestershire County Council has said it will resort to using table salt to treat roads.
The BBC Weather Centre said some parts of the UK, including Kent, Shropshire, Northern Ireland and north west Wales, woke up to a fresh covering of snow on Saturday.
Further snow is likely to fall in the north east of England but is not likely to cause major disruption, while overnight into Sunday temperatures are expected to fall to -10C in rural areas and -4C to -7C in city centres.
Snow and ice create havoc on the roads on Friday
Falling temperatures in the Bristol and Bath region have meant that roads and pavements are frozen. The Highways Agency and Great Western Ambulance Service have urged people to stay at home.
Police forces across the West Country have advised motorists to only make journeys if they were essential, as many roads were covered in black ice.
The M4 bridge crossing the Severn and the M48 Severn Bridge were closed for a time, due to concerns over falling ice, but both have now reopened.
Roads across Wiltshire were particularly badly affected.
Forecaster Tomasz Schafernaker said: "From Sunday morning almost anywhere in the UK may get a further covering, with the north more likely to see snow, up to four inches over the hills.
"On Monday into Tuesday, southern Britain is at risk of a further dumping of snow."
Some councils in England have been running out of road salt, with the Highways Agency saying supplies were "very limited".
Gloucestershire County Council has ordered 500 tonnes of white table salt from a company in Cheshire.
It is alarming that we face a grit shortage as the country has to contend with more snow and freezing weather
Authorities in Wiltshire hoped to get 500 tonnes of salt from Devon County Council.
Stocks in west Berkshire are at 20% of normal levels and are expected to last only another two or three days.
Cheshire-based Salt Union said staff were working around the clock but still could not meet demand.
A container ship is travelling from Spain with 40,000 tonnes of salt, and another ship is also heading to the UK with salt from Germany. Both are expected to dock on Wednesday.
Meanwhile, the Irish Salt Mining and Exploration company in Carrickfergus, Antrim, is digging up to 6,000 tonnes of salt a day, having been inundated by calls from councils across the UK.
The BBC's Alex Bushill in Bristol said many councils in the west of England have recently taken salt deliveries and that the situation is now better than it was on Thursday, when supplies were being effectively rationed.
Paul Bettison, chairman of the Local Government Association (LGA) Environment Board, said eight councils had to prioritise supplies to focus on the most important roads.
He said: "If that fails to deal with any issue, then councils will talk to the Highways Agency to look for further supplies."
Neil Robertson sent this shot of a snow plough crash near Tomintoul, Scotland
But Theresa Villiers, shadow transport secretary, said: "It is alarming that we face a grit shortage as the country has to contend with more snow and freezing weather."
Paul Watters, head of roads policy at the AA, said: "The 40,000 tonnes coming on the ship from Spain does not sound a lot - just one salt run can be 130 tonnes, and you have to think of all the different authorities that are involved.
"We certainly don't seem to be out of the woods with the weather, they're saying there could be some more snow on Monday.
"It's just crazy that we couldn't have realised that we were going to enter this situation so we could arrange supplies before we had the problem rather than during it."
Jacquie Stares, 58, from Exford in Somerset, told the BBC there was still two feet of snow in her front garden, but that it was "thawing fast".
She added: "It's so deep that it's going to take some time to thaw, but it is on its way.
"The village shop has been rationing supplies but everybody around here has been sensible and has stocked up on items like bread and Calor gas, just in case."
In Somerset there are 1,000 homes without power after snow and ice made access to necessary power line repairs difficult. Western Power says it hopes to have restored electricity by the end of Saturday.
A man is in hospital in Swindon with serious head injuries after a gang of teenagers beat him unconscious when he asked them to stop throwing snowballs at his car.
Bath's Royal United Hospital has cancelled orthopaedic surgery for the weekend because its staff have struggled to get to work.
Monday's race meeting at Wetherby has been abandoned after the track failed an inspection.
Northamptonshire Police said the freeze had left roads in the county in a treacherous condition.
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