Over the next few days it will be bitterly cold by day and temperatures will plummet as low as -7C at night.
Last night they dropped to -10C in Mullingar and at Dublin airport.
But the worst of the heavy snowfalls, which caused traffic chaos across Dublin, Kildare, Wicklow, Kerry, Cork and Limerick, are behind us.
It will be drier from tonight with clear skies, although this will give rise to severe frosts and freezing fog.
The mercury tonight will drop to between -1C and -6C with scattered rain, sleet and snow.
"Slack winds will lead to freezing fog in places and there will be ice on untreated roads," according to Met Eireann's Siobhan Ryan.
"Wednesday and Thursday will see a lot of dry weather and it will be cold, although bearable if you wrap up well, but it will be bitterly cold by night", she added.
Age Action Ireland has urged people to check on pensioners over the next few days.
Motorists have been warned to expect treacherous driving condition for the rest of the week, particularly at night.
Last weekend the AA dealt with more than 1,000 motorists stranded by floods, icy and snow-covered roads and batteries that had failed.
Dozens of flights have been cancelled or delayed because of heavy snowfalls across much of the continent; those intending to travel have been asked to contact their airlines.
Tomorrow gets off to a frosty and icy start, but will be dry in most areas with sunny spells and temperatures lifting to as high at 8C.
By night a severe frost will develop with ice and some freezing fog while temperatures drop back to -7C.
Thursday will be dry but very cold, with highest temperatures reaching between 2-4C.
By Friday there will be some heavy rain but with temperatures easing to between 5-9C and warmest in the south.
The rain will continue on Saturday, and Sunday will still be rather cool with sunny spells and showers, mainly affecting Atlantic counties.