The fatality occurred when a car collided with a bus near Turku in the southwest, officials said.
Flight delays and cancellations were reported at Helsinki's Vantaa airport, while ferries between Helsinki and the Estonian capital Tallinn stopped running due to high winds at sea.
"It's chaos in the capital," said Helsinki police spokesman Jussi Pohjonen.
Finland's meteorological service advised motorists to be careful as it forecast up to 30 centimetres (12 inches) of snow to fall across the southern third of the country overnight into Thursday.
Finland had been enjoying one of its mildest winters on record, with temperatures between four and six degrees Celsius (39 to 42 degrees degrees Fahrenheit) above average.