Temperatures as low as -7 degrees are expected overnight, as very cold weather continues.
Lowest temperatures of -2 to -5 degrees are being forecast for the country, but may fall even lower in some parts of Connacht and Ulster.
A status yellow low temperature/ice warning is in place for Connacht, Cavan, Monaghan, Donegal, Longford and Clare from 6pm tonight until 10am tomorrow.
Status Yellow - Low Temperature/Ice warning for Connacht, Cavan, Monaghan, Donegal, Longford and Clare https://t.co/Xg3aMJlyuS
Valid: 18:00 Tuesday 05/01/2021 to 10:00 Wednesday 06/01/2021
Issued: 13:00 Tuesday 05/01/2021
Updated: 13:22 Tuesday 05/01/2021 pic.twitter.com/YRZ8nByHzZ
— Met Éireann (@MetEireann) January 5, 2021
An ice warning is also in effect for Antrim, Armagh, Down and Tyrone.
Met Éireann says Tuesday night overall will be very cold, with widespread severe frost and ice.
It will remain dry in most areas, but scattered wintry showers of hail, sleet or snow are possible in eastern and southeastern counties.
The frost and ice is expected to linger in some areas throughout Wednesday, with temperatures staying below freezing in parts of the midlands and west.
The extremely cold weather is set to continue throughout the week, with temperatures "well below normal".
However, it's then expected to become less cold over the weekend.
Alan O'Reilly of Carlow Weather said most places will be below zero degrees tonight, and could reach -6 or -7 degrees.
He told Lunchtime Live: "What's probably going to bring more snow to more low-lying level is a band of rain that's going to move in tomorrow night to early Thursday morning.
"It will die out fairly quickly as it starts to cross the country, but it will fall as snow - particularly in the north-west or midlands.
"You will have many people in the north-west and midlands waking up to a dusting there - a couple centimetres possibly on Thursday morning."
He said these sort of cold weather conditions don't always mean heavy snow like a 'Beast from the East' situation in 2018, but it does increase the chances.
While the weather may improve next week, Mr O'Reilly added there's always the chance of a quick turnaround back to colder weather as we head into the end of January and start of February.