The frigid temperatures, down to minus 24 degrees Celsius (minus 11 degrees Fahrenheit) in parts of Germany and minus 29 in Estonia overnight, have prompted warnings for the most vulnerable homeless and elderly.
Cities across the continent have been providing emergency shelter and relief to rough sleepers, who accounted for most of the deaths since Friday.
Poland has reported at least nine deaths with four in France, including an nonagenarian who was found Tuesday outside the gate to her retirement home. Five have died in Lithuania, three in the Czech Republic and two in Romania, including an 83-year-old woman found on the streets covered in snow, and one homeless person in Italy.
The frigid weather was set to continue Wednesday, with temperatures down to minus 12 C expected in northen France and minus 6 C in the usually mild south.
More snow was forecast for Spain, including Catalonia where school transport has been cancelled. Classes have also been suspended in the Canary Islands which is being lashed by powerful winds.
While the Arctic is seeing record high temperatures, the cold snap across Europe has brought snow even to the balmy Mediterranean islands of Corsica and Capri.
In Belgium, towns including Etterbeek, Verviers and Charleroi have resorted to ordering police to detain homeless people if they refuse to go to shelters.
The Red Cross, which has set up emergency teams across Europe, urged people to keep an eye on neighbours and relatives.
"Just knocking on someone's door to check they have everything they need can make a huge difference. It could even be the difference between life and death," it said.
The charity also issued public appeals for 10,000 blankets in France, where about 50 local officials in the Paris region have vowed to spend Tuesday night outdoors to call attention to the plight of those with nowhere to sleep.
"The point is not to stage a show, but to denounce a system that isn't working," said Mama Sy, a deputy mayor in the Paris suburb of Etampes.
Paris authorities counted 3,000 rough-sleepers in the city's first-ever homeless census this month, warning it was likely significantly underestimated.
In England, where heavy snow was dumped on London Tuesday, tabloids have dubbed the snap "the Beast from the East", while the Dutch are calling it the "Siberian bear" and Swedes the "snow cannon".
British Airways cancelled roughly 60 flights in and out of London Heathrow airport.
The Met Office forecaster said rural communities could be cut off for days by snowdrifts, warning of "long interruptions to power supplies and other services such as telephone and mobile phone networks."
Some of the iciest conditions were reported in Italy, where many schools and daycare centres were closed, to the consternation of parents already preparing for closures next week linked to this weekend's general election.
Italians' anger was also growing over nationwide disruptions to rail services as a lack of defrosting equipment on the tracks meant workers having to clear snow and ice by hand.
In Naples, the airport was closed early Tuesday and bus services in the city halted because of ice, though the weather was getting warmer in Rome, where schools were expected to reopen Wednesday.
A driver in Turin got a fright when an ice shard broke off from an overhead bridge and shattered his windshield though he managed to keep control of his vehicle.
Russia's Gazprom, a major gas supplier to Europe, said it had sent record exports to the continent over the past six days, peaking at 667 million cubic metres (23.6 billion cubic feet) on Monday as people turned up their thermostats.
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