Met Éireann has warned of dangerous travelling conditions as a Status Yellow warning for low temperatures and ice remains in place for the entire country.
The forecaster has said that “very cold” nights with widespread frost and ice are expected in the coming days, with the warning in place until midday on Thursday.
Temperatures will struggle to rise above freezing during the day.
Icy patches on roads and disruption to travel are also expected.
It comes amid a cold snap which swept many parts of the country over the weekend, when a Status Orange Snow-Ice warning, and a Status Orange Snow and Rain warning, were in place for many counties in the south and midlands.
Those travelling in the coming days have been advised to plan their journey in advance, take extra time, and slow down.
Met Éireann has said some sunshine and scattered showers of rain, hail, sleet and snow are expected today, with top temperatures generally ranging from 1-5C.
Iarnród Éireann has said that the Nenagh branch line (Limerick to Ballybrophy via Nenagh) will not be in operation this morning.
Bus Éireann announced a series of full service cancellations including on route 13 from Tralee to Limerick via Listowel, route 40 from Tralee to Cork via Killarney and all route 270 services.
Selected services have also been cancelled this morning on several other routes including routes 233, 236, 237, 239, 245 and 257, 275 and 279 in the south of the country.
Dublin Bus, meanwhile, confirmed its 44b service is unable to serve Glencullen in south Dublin.
Some of the country’s hospitals have warned patients not to attend due to the challenging weather conditions.
The HSE has cancelled some services in Cork, Kerry, South Tipperary, Laois and parts of the Mid West, including outpatient appointments and day services.
The cancellations include all non-urgent outpatient appointments at Cork University Hospital, South Infirmary Victoria Hospital, Mercy University Hospital, Bantry Hospital and Mallow Hospital.
However, ante-natal appointments will go ahead at CUH.
At this point, there are no disruptions in the West and North West, most of Dublin, and the North East, the HSE said.
A number of schools will remain closed following the Christmas break due to adverse local weather conditions.
It is expected that almost all schools in counties Carlow and Kilkenny will remain closed, while authorities have said that decisions will be made locally by school leaders.
The Carlow Institute of Further Education and Training campus will also remain closed.
In Cork, primary and secondary schools in Mitchelstown, Doneraile and Glanworth will not open.
Thousands remained without power overnight, as the latest figures from ESB Networks show 40,000 homes, farms and businesses are without power, mostly in Cork, Kerry, Limerick, Tipperary and Laois.
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Uisce Éireann said around 41,000 premises remain without water, predominantly in Tipperary, Limerick, Kerry and Cork.
It said another 30,000 are at risk of water loss due to low reservoir levels with crews working to maintain and restore supplies.
It urged households, businesses and farmers to check for leaks and turn off water to outside pipes or unoccupied premises.
The water service also suggested that people consider setting the heating for these areas to come on periodically at a lower temperature, which allows warm air to circulate and will help to prevent pipes and tanks from freezing in the cold weather.
Roads
Gardaí in Co Tipperary yesterday dealt with a number of calls from motorists experiencing difficulties on off-ramps from the M7 motorway.
The problems were particularly pronounced at Junctions 23 and 24, around Moneygall and Toomevara, where compacted snow and slush left exit ramps extremely difficult to navigate.
A number of vehicles were stuck on the slip roads there, causing delays on the motorway in both directions.
Roads around Emly, Kilross and Bansha were covered by several centimetres of snow.
Transport Infrastructure Ireland snow ploughs worked to clear the M18 between Limerick and Ennis, where heavy snow led to delays.
Most major transport arteries in both Limerick and Clare are passable but extreme care is advised on secondary roads, particularly on higher ground.
Gardaí say that the forecasted drop in temperatures will further complicate the situation on such routes.