Rescue crews, including the army and fire brigade, were working to evacuate people stranded in their cars on an Athens motorway and main thoroughfares.
More than 3,500 people had been evacuated by early Tuesday, some abandoning their cars on foot, while around 1,800 cars remained stuck on the motorway, the capital's main ring-road.
People evacuated from the motorway were sheltered at the Athens Airport hotel overnight.
"As you can imagine, it was so cold, so cold," said driver Giorgios Fragkoulis, who spent the night in his car on the motorway.
Soldiers and fire-fighters with shovels were being assisted by bulldozers to try and dig out the vehicles.
"The situation is hopeless. They should be ashamed for this mess," said driver Spiros Kandaras, who spent the last 24 hours in his car.
Authorities declared Tuesday and Wednesday a public holiday, keeping only non-essential services such as supermarkets, pharmacies and petrol stations in the greater Athens area and on some islands open.
The storm, named Elpida, was forecast to persist until Wednesday.