Temperatures dropped to as low as -26C (-14.8F) in Poland, where eight people died of exposure. Five others died in central Europe and two in the UK.
London's Gatwick airport remains closed, while many flights have been cancelled in France and Germany.
Eurostar has meanwhile had to cancel half of its services on Thursday.
The freezing conditions will continue for days as the low-pressure front centred over Western Europe moves slowly eastward.
"We've got unusually cold air over large parts of the eastern Atlantic, and where that meets warm air coming for example from the Mediterranean you have a lot of snow," said Heinz Maurer of Meteosuisse, the Swiss national weather service.
He predicted that snowfall would ease in central Europe by Thursday.
Widespread snowfall forced several airports, including Gatwick and Durham Tees Valley in England, Edinburgh and Dundee in Scotland, Geneva in Switzerland, and Lyon-Bron in France to close on Wednesday.
Geneva airport reopened on Thursday morning, but was advising that passengers arrive a full two hours before the departure time and use public transport to avoid traffic problems on the roads. In the UK, Gatwick delayed opening until at least 0600 GMT on Friday, further stranding about 600 flights that were scheduled to leave on Wednesday.
The French civil aviation authority has asked airlines to cancel 25% of the flights due to depart from Paris Charles de Gaulle and 10% of the flights out of Paris Orly on Thursday in anticipation of further problems.
Europe's busiest airport, Heathrow, is also warning of disruption. Frankfurt, Munich, Vienna and Prague airports were affected on Wednesday.
It is also expected to be another day of delays and cancellations on rail services across Europe, and of widespread problems on roads.
In France, 12 regions in the frozen east and centre banned the use of lorries, forcing more than 7,000 of them to park overnight, while the weather has caused hundreds of accidents on German roads.
Polish police have been carrying out patrols to find homeless people and get them into shelters. Eight homeless men died of exposure on Tuesday night after temperatures fell to about -20C (-4F). Most had been drinking.
In northern Austria, a 69-year-old pensioner froze to death overnight after slipping on a snow-covered bridge on his way home from a funeral.