Police said on Sunday that there was heavy traffic on the Karvounas-Troodos-Platres road and urged motorists to drive cautiously and to comply with traffic signals and police instructions.
The depth of snow in Troodos Square was 21cm on Sunday, the met office said.
More snow is forecast to fall in the mountains on Sunday night.
For the remainder of the island, it is expected to me mainly cloudy with some isolated showers in western regions.
Temperatures will drop to 6C inland, around 10C on the coast and to 1C in the higher mountains.
On Monday the weather will be partly cloudy with the possibility of isolated rains mainly in the west, while in the higher mountains light snow or sleet is likely.
During the day, the temperature will rise to around 18C inland and on the coasts and 9C in the higher mountains.
On Tuesday, Wednesday and Thursday the weather will be mostly cloudy with isolated rains, while the mountain areas can expect more light snow or sleet.
Temperatures will fluctuate at the same levels, which are close to seasonal averages.