1118 GMT January 18, 2021
Madrid, one of the worst affected areas, is set to see up to 20cm (eight inches) of snow in the next 24 hours, BBC reported.
Further south the storm caused rivers to burst their banks.
Interior Minister Fernando Grande-Marlaska told a news conference that three deaths had been reported so far.
A 54-year-old man was found dead under the snow in the town of Zarzalejo, northwest of Madrid, El Pais newspaper reported, and two other people were said to have been swept away by floods near the southern city of Malaga.
As snow fell on Madrid on Friday evening, a number of vehicles became stranded on a motorway near the capital.
The city's Barajas airport has closed, along with a number of roads, and all trains to and from Madrid have been canceled.
Firefighters were called in to assist drivers who had become stuck. In some areas the military were called in to help clear roads.
Spanish Prime Minister Pedro Sánchez urged people to stay at home and to follow the instructions of emergency services.
According to local media, the snowfall in Madrid is the heaviest in at least 40 years. The country's AEMET weather agency said the snowfall was "exceptional and most likely historic".