Sub-zero temperatures will affect almost all of the county over the coming days, with air temperatures plummeting to minus five degrees in some areas, according to Met Éireann.
The cold snap is due to continue for much of the week, Met Éireann forecaster, Ms Joan Blackburn said, with widespread frost and the possibility of snow.
The weekend saw night-time temperatures drop to between minus three and minus five degrees across the midlands and north of the country. Only some coastal fringes in the east and south-east remained above freezing. Belfast was particularly cold, with air temperatures of minus 4.1 degrees and ground temperatures hitting minus 10 degrees.
Similar temperatures are expected throughout the week, Ms Blackburn said. "By and large we can expect very cold weather and when the skies are clear, it will be very frosty. Although there won't be any great quantities of precipitation there might be flurries of snow."
Sunny periods during the day could "disguise the cold a little", she said, but the nights will be particularly cold. The chances of very severe frosts overnight will depend on the levels of cloud cover.
"It's looking a bit messy at the moment, the cloud may come and go overnight and when it is cloudy there is little danger of frost, but if it's clear, it will be frosty."
The winter has been "fairly benign" since the storms last Halloween, with temperatures a degree higher than normal across the country and rainfall below normal everywhere apart from the north-west.
Recent high winds are unlikely to re-emerge this week and conditions, while cold will be calm."It's certainly quietened down, but it is a cold snap."
Meanwhile, severe blizzards across the north-east of the US could lead to the cancellation of flights to major US cities this week.
One flight from New York to Shannon and Dublin was cancelled yesterday, following a delay of more than 12 hours. Five flights to New York from Dublin were delayed by more than four hours in Dublin airport yesterday, but there were no further cancellations, an Aer Rianta spokesman said.
However, US weather reports forecast further heavy snowfalls in New York, Boston and Philadelphia.
A security alert at Dublin airport on Saturday evening did not result in any flight delays, the spokesman said.
The alert was called after a suspicious powdery substance was found in a bag in the arrivals area of the airport. The bag was removed for examination by the fire brigade.
Tests were being carried out on the powder yesterday. However, the spokesman said he could not comment on the powder's contents for security reasons.
