Met Éireann has issued a nationwide warning for snow and freezing temperatures over the next 24 hours.
It has issued a “status orange” warning of hail, sleet and snow in the west and north-west.
Up to eight cm of snow is likely on high ground in Connacht and west Ulster. The weather warning is in place until tomorrow morning.
A separate "status yellow" warning is in place for Leinster, Cork, Tipperary and Waterford.
It has forecast wintry showers of hail and sleet along with icy patches on roads and footpaths funtil Wednesday morning. Snow of up to 4 cm is likely on high ground.
Motorists across the country have been advised to take extra care on roads and to watch out for “black ice”, one of winter’s worst road hazards, which occur especially in sheltered or shaded areas on roads.
Icy patches will form in any locations escaping snow showers. The alert said that further snow showers and similar accumulations will occur during today and later tonight.
Yellow alerts are issued for weather conditions that do not pose an immediate threat to the general population, but present risks for some due to the nature of their location or activity.
An orange alert is issued in cases where adverse weather has capacity to impact significantly on people in the affected areas.
While the alerts are due to last until tomorrow morning, the snow is forecast to be followed by a storm depression which will bringing scattered thunderstorms and sleet in places on Wednesday and into Thursday. The disturbed weather pattern is set to ease on Friday.
The cold spell follows a weekend of blustery conditions and high winds which left over 2,150 households without power yesterday morning.
The ESB is continuing to work to resolve the power faults, which were worst in counties Cork, Limerick and Galway.
Strong winds disrupted a helicopter rescue off the southwest coast. The Valentia coastguard was called to rescue an injured fisherman off the coast of Mizen Head, but the Shannon rescue helicopter was unable to lift-off due to high winds and a large sea-swell.
The Waterford rescue helicopter was instead tasked with rescuing the man, who has regained consciousness and whose condition has improved.