In France, flights were delayed by an average of an hour in Paris's Orly and Roissy-Charles de Gaulle airports.
One of Orly's two runways was closed, while the other opened two hours late.
Air France cancelled around 30 short- and medium-haul flights from Charles de Gaulle on Monday morning, but said long-haul routes had not been troubled.
The country's road traffic agency urged motorists to cancel non-essential journeys.
At London's Heathrow airport, snow caused a Cyprus Airways jet with 104 passengers on board to come off the taxiway.
A spokeswoman for airport operator BAA said: "The plane had safely landed and was making its way to the stand and the front wheel went on to the grass area,"
Passengers were transported to the terminal and there were no injuries.
Both runways have since been closed at Heathrow, while all flights were cancelled up to 1700 GMT.
British Airways has called off all its short-haul flights for the rest of the day.
A number of other British airports were closed or had severe delays and flight cancellations.
Forecasters at Britain's meteorological office issued a severe weather warning for the capital and the southeast of England, with train and London underground services badly hit.
Hundreds of schools closed around the country as an army of snow ploughs and gritters worked to clear roads.
Up to 20cm also fell in parts of Switzerland overnight, while part of the road around the San Bernardino tunnel was closed.
Snowfalls snarled traffic in several parts of Spain, including the Madrid area, where sections of two highways were temporarily closed to vehicles, causing traffic jams.
In Ireland, snow caused hazardous driving conditions there and flights between Ireland and Britain were disrupted.