Police are warning drivers to be particularly careful as roads are slippery because of the rain.
Snow has fallen in the mountains where there is thick fog and visibility is low, they added.
The Karvounas-Troodos, Prodromos-Troodos and Platres-Troodos roads are open only to vehicles with four wheel drive or equipped with snow chains. Elsewhere on mountain roads there have been mud and rock slides.
Drivers are urged to be particularly careful, to drive slowly, keep a safe distance from other vehicles and switch on their headlights.