Schools and childcare facilities in parts of the country will stay closed or open late on Monday as icy conditions persist and regional snow and sleet warnings remain in place.
All parts of the country are to remain extremely cold into Tuesday but the north west and north are most at risk of wintry showers.
Management at schools and preschools in parts of Co Donegal including Letterkenny, Buncrana, Milford and Carndonagh have taken the decision not to open for what was to be the first day back after the Christmas holidays.
Others are opening with delayed starting times. More than 160 schools in Northern Ireland will also stay closed.
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Schoolbus routes served by McGettigan Travel are also cancelled and the company says it will make a decision on Monday evening about whether to run services on Tuesday.
Inland areas of Co Donegal received repeated snow showers over the weekend with little thaw and further falls last night added to the accumulation.
Some schools and childcare providers in Cork City and county are also opening late to allow for snow to clear and overnight ice to thaw.
Parents are being advised to check school apps and emails for notifications.
A status yellow low temperature and ice warning is in place for Leinster, Munster, Cavan, Monaghan, Galway and Roscommon until 9am on Tuesday.
A yellow snow and ice warning has also been issued for Donegal, Leitrim, Mayo and Sligo until 9am on Tuesday.
Met Éireann said there will be cold and dry spells on Monday night, though wintry showers will become more widespread in the north for a time early on.
Widespread frost and icy stretches will form early on along with patches of mist and fog. Lowest temperatures will be between minus three to two degrees overnight, with light to moderate westerly winds backing southwesterly by morning.
The forecaster said it will be cold and dry to start in the eastern half of the country on Tuesday morning, with frost and icy patches.
Outbreaks of rain and drizzle in the west will move eastwards through the morning and early afternoon, becoming patchier as they do. Sunny spells and scattered showers will follow.
Highest temperatures will range from three to eight degrees, with coldest conditions in the east.
Any showers along Atlantic coasts will ease early on leaving dry conditions with clear spells on Tuesday night. Lowest temperatures will be between minus one to three degrees with light to moderate northwesterly winds.
Patchy rain and drizzle will spread across the country from the west, possibly turning to sleet over higher ground on Wednesday. Highest temperatures will be between three to five degrees in the east and northeast, but milder in the west and south with highest temperatures of five to 9 degrees.
Met Éireann said rain is likely to spread over the southern half of the country with scattered showers further north on Thursday. Highest temperatures will range from three to seven degrees with mostly light westerly or variable winds.
Friday will likely see a mix of sunny spells and showers, mainly affecting Atlantic coastal counties.
The forecaster said current indications show unsettled conditions for the weekend with a signal for some wet and blustery weather.
