Weather agency AEMET has forecast accumulations of between 3 and 5 centimetres.
Drivers should not head out without snow chains or winter tyres, the agency warned.
Some 33 provinces have been placed on red, orange or yellow severe weather alerts today.
Most of them are in the north of the country.
But there are also alerts for freezing temperatures, strong winds and high coastal waters down south and in the Balearics.
Menorca will be on orange alert for maritime storms, while Ibiza, Mallorca, Formentera, Alicante, Almería and Granada will be on yellow alert for high coastal waters.
Meanwhile, AEMET has predicted up to 90% of the peninsula could be hit by several days of freezing temperatures on Monday.