Temperatures are expected to drop to below freezing tonight but will return to near normal next week.
Sunday will be coldest in the east with temperatures between 3C to 6C while it will be warmer elsewhere – closer to 7C to 10C.
Met Éireann said there will be outbreaks of rain and possibly sleet in the early part of the morning but it will brighten up by afternoon with sunny spells developing.
Tonight, temperatures will drop to lows of between -2C and 5C.
It will be coldest across Leinster and Ulster with some frost and ice expected.
There will be some mist and fog in parts and it will become cloudy overnight with patchy light rain developing in the west, spreading eastwards later.
On Monday, temperatures “will return to more near normal everywhere”.
The day will see “further patchy outbreaks of rain, mainly confined to the northwest by afternoon.
Met Éireann said it will be “generally cloudy to begin with some sunny spells later.
“Once again, mist or fog will occur in parts through the day. Highest temperatures will range 9C to 11C, in mostly moderate westerly breezes.”
The rest of the week will see some milder days but Met Éireann said that overall it will be “rather cold and unsettled”.
The cold weather comes as Storm Arwen caused significant disruption in the North and the UK.
A man in Antrim died on Friday after his car was struck by a falling tree.
He was later named as Francis Lagan, principal of St Mary’s Primary School in Maghera, who died after the incident on the Dublin Road in Antrim on Friday as high winds hit the area during Storm Arwen.