Yellow warnings for snow and ice remain in place until Saturday for much of the UK, apart from southern England.
"With clearing skies and snow on the ground, temperatures tonight will drop like a stone," said BBC weather forecaster Matt Taylor.
He said icy conditions would be an issue in many areas.
Some rural areas in Scotland, England and Wales could see temperatures of -10C to -13C overnight into Saturday.
National Highways operational control director Andrew Page-Dove said there was a risk of potentially freezing rain and more snow.
"The conditions are actually going to get worse rather than better," he said.
Heavy snow overnight into Friday in parts of Wales and north-west England caused disruption including long delays on the M62 trans-Pennine motorway.
Drivers reported stationary traffic on the eastbound carriageway between Rochdale in Greater Manchester and Huddersfield in West Yorkshire.
By midday, congestion stretched for around 17 miles after two lanes were closed between junctions 20 and 22.
Mr Page-Dove said the traffic chaos was down to a "combination of volume of traffic and [drivers] maybe not being as well prepared for the conditions".
National Highways gritters were delayed on the M62 by stranded lorries unable to cope with the conditions, he added.
Confirming that the M62 would remain open, he said: "We have well-rehearsed plans which we execute every time we have these types of events."
Dozens of people took to social media early on Friday, describing spending hours stuck in standstill traffic on the motorway.
One woman who got stranded on a nearby road told the BBC she had "never seen anything like it" and had to be helped by mountain rescue.
Kim Ward was on her way home from to Halifax from a concert in Manchester overnight with her sister-in-law, niece and a friend.
She told the BBC: "The M62 was shut, so we thought we would take the A-road.
"We thought we would be alright, but as we got higher and higher, it just got worse and worse.
"We spent a couple of hours completely stuck, freezing - we actually started nodding off in the car.
"Next thing we knew mountain rescue were knocking on the window with their torches."
Ms Ward continued: "I have been on numerous ski holidays, but I have never seen anything like it, up on the top there.
"It's scary, thinking you are going to actually spend the night here in the car."
The winter weather has been named Storm Larisa by the French weather service.
On Friday, more than 200 schools shut their doors in Wales, while in Northern Ireland, more than 100 were closed as a result of the snow.
In England, hundreds of schools across North, South and West Yorkshire, as well as the West and East Midlands, Lancashire and Greater Manchester, were also forced to close.
Some schools were closed on Thursday in Aberdeenshire, in Scotland, but Aberdeenshire Council said there were no planned closures for Friday.
Milder air is forecast for Sunday into Monday when a thaw will begin and conditions will start to improve.
Yellow weather warnings are issued when severe weather that could cause disruption to everyday life is possible, according to the Met Office's website.