The freezing spell is set to continue across the UK throughout the week with temperatures expected to reach minus 8C.
On Monday, temperatures fell to their lowest levels since 1986, reaching minus 13C, and hundreds of motorists were left stranded across Sussex roads for up to eight hours due to icy and snowy conditions.
Sussex Police said it had attended more than 300 accidents in 24 hours and was urging people not to travel unless it was necessary.
Chief Inspector Phil Nicholas said: "The conditions meant there was a significant demand on our resources last night and we were stretched to capacity.
"Today is going to be about helping recover vehicles as many people fell asleep in their cars or abandoned them so even when the roads did become clearer they were still blocked by many vehicles.
"We will be assisting the Highways and other partner agencies to recover these vehicles. Although the conditions have improved slightly, we are asking people to not make any journeys unless they are essential."
Gatwick Airport has warned passengers to leave extra time for their journey to the airport because of the snow. Most flights to the Channel Islands have been cancelled.
Schools across Essex and Norfolk have closed today, while over 150 schools in Sussex have been forced to shut due to the adverse weather.
The Met Office said there was a 100 percent cancer of severe cold weather, with icy conditions and heavy snow predicted between Sunday and Thursday.
It put an amber alert out, meaning people should be prepared for extreme conditions. It also warned that the cold weather can be dangerous for very young or old people, and those with chronic diseases.
Leon Brown, chief meteorologist at uk.weather.com, said the south of England will remain "bitterly cold" with a wind chill equivalent to -3C or -4C.
He explained that Wednesday will begin with a widespread frost and up to 8cm of snow can be expected over the North York Moors, while the temperature will then start to fall again.
Meanwhile other parts of Europe have been experiencing similar weather conditions.
A quarter of flights from Paris have been cancelled and there are delays on the Eurostar, while Belgium is suffering from record traffic jams spanning around 1,600km
French train network SNCF urged commuters not to travel to Paris today, while trains from Belgium were cancelled, including high speed trains to France, Germany and the Netherlands.