Met Éireann has issued two new Status Yellow warnings, one for low temperature/ice and another for snow/ice, as a number of schools remain closed in parts of the country.
Around 180 primary and secondary schools in Northern Ireland and all those in the Finn Valley area in Co Donegal did not reopen this morning after the Christmas break due to severe weather.
The forecaster has issued a new Status Yellow - low temperature/ice warning for Leinster, Cavan, Monaghan, Munster, Galway and Roscommon, which is in place until 9am tomorrow.
The warning says temperatures will fall between -1C and -3C with sharp frost, icy stretches and the possibility of black ice.
The second new Status Yellow warning issued by Met Éireann is for snow-ice for counties Donegal, Leitrim, Mayo and Sligo, which is in place until 9am tomorrow.
Wintry showers with sleet and some snow accumulations, with sharp frost and ice are expected.
While the Met Office UK has issued a new Status Yellow ice warning for Antrim, Armagh, Down, Fermanagh, Tyrone and Derry, which is due to come into effect from 5pm this evening until 10am tomorrow.
"Ice formation on untreated surfaces is likely to cause impacts in places on Monday evening, and overnight into Tuesday morning," the UK forecaster said.
Treacherous conditions
Met Éireann is warning of sharp or severe frost and icy stretches, black ice too and treacherous travel conditions.
Meteorologist Ailís Hankinson said widespread frost and ice will be very slow to thaw and that patches of freezing mist and fog are adding to the danger.
She said that road surface temperatures dropped below freezing across the country while air temperatures were below freezing at most weather stations.
Some road temperatures dropped as low as -6C, while in the midlands region air temperatures were as low as -4C and -4.5C.
The lowest temperature recorded was -7C in Katesbridge, Co Down.
Driving conditions remain challenging across Donegal, according to Director of Roads and Transportation with Donegal County Council Bryan Cannon.
He advised the public to avoid unnecessary travel and said the main road network is passible with care, but warned that some roads such as those on higher ground are "more challenging".
"These are Barnesmore gap, Glenties and Letterkenny," he said, adding that rural roads are the issue.
"When driving, they should assume that no road is ice-free."
He said that crews were out since 5am gritting 1,100km of roads but there were fresh accumulations of snow yesterday evening and overnight.
Mr Cannon added that there is a continuous winter service to grit the network.
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The PSNI urged road users to take extra care, especially in areas which may not have been gritted due to wintry conditions.
"Clear your windscreen before you set off on your journey, and remember to slow down and increase the distance between you and the vehicle ahead," they said.
Bus Éireann said several services had been cancelled or delayed due to icy road conditions.
Countrywide, temperatures will not get back up above freezing until closer to midday and are expected to drop again early tonight, Ms Hankinson said.
