Night-time temperatures will go as low as -4C and strong northerly winds by day will bring an extra chill.
It's time to dig out the winter woollies as Arctic winds will see temperatures during the day of between 5 and 8C.
By night, these will fall to -3 or -4C.
Met Eireann says severe frost will settle across many parts and there will be patches of freezing fog, with sleet on higher ground towards the end of the week.
By Thursday "outbreaks of rain will reach western counties and these will spread slowly east to affect most other parts of the country by the end of the day; in mountainous areas, the rain may turn to sleet occasionally", Met Eireann said.
Weather warnings remained in place today as motorists were told to be particularly careful of frost and black ice.
While some showers were expected, most of the heavy rainfall which caused flooding overnight yesterday in Dublin and other eastern counties had moved off.
Met Eireann said it will be dry and clear tonight but temperatures will be as low as -2 degrees, with widespread ground frost and icy patches expected.
The cold weather overnight and into this morning meant more workers opted for their cars to commute today.
The AA's Rebecca Horan told the Herald traffic was very heavy this morning as she believes drivers did not know what to expect with the recent bad weather and are taking their time.
In the coming days when it gets colder, drivers need to make sure they slow down, she added.
"Gentle manoeuvres and taking extra care are the key to safe driving. Drivers need to reduce their speed and keep a safe distance from their vehicle in front," Ms Horan said.