Met Eireann's Status Yellow ice and snow warning remains in place this morning with conditions set to turn sub-zero later this evening.
The alert, which covers the whole of the country, began at 9am on Sunday and will stay in place until 10am on Monday.
While forecasters are now warning that the cold snap will continue, with temperatures plummeting as low as -3C tonight.
But there is some good news, as temperatures are set to increase to highs of 10C later this week.
More fog and ice is expected tomorrow, with further freezing conditions in the forecast for Tuesday night.
A Met Eireann forecaster said: "This morning will start cold with frost and icy stretches in many areas and some mist patches.
"Showers, some heavy and wintry on hills will affect Western parts of Ulster, Connacht and Munster today but elsewhere there will be a good deal of dry weather with some winter sunshine. Top temperatures just 3 to 6 degrees.
"Tonight, further showers in the West and North, some wintry. Mainly dry elsewhere.
"Cold with a widespread frost, icy patches and some freezing fog patches. Lowest temperatures as low as 0 to minus 3 degrees as winds fall light.
"Tomorrow will be a mainly dry day with sunny spells and temperatures of between 2 and 6 degrees at best with light winds. The odd shower may still affect some Atlantic coastal parts, and fog may linger in places.
"Tuesday night will be mainly dry and very cold with lowest temperatures of zero to minus 2 degrees with frost and icy stretches forming quickly after dark.
"Some mist and fog patches forming for a time also. Later in the night Southeast winds will freshen near Atlantic coasts bringing rain to the Southwest by dawn."
However the forecast will improve as the week goes on, as temperatures will start to pick up with highs of 10C possible during the day on Thursday, although further frost is expected at times overnight.
A forecaster added: "On Wednesday, the rain and freshening Southeast winds will spread up over the country reaching most places by mid-afternoon.
"Western counties should turn drier again later in the day but heavier pulses of rain look likely to feed into Eastern parts during the evening.
"There'll be a rise in temperatures to between 7 and 9 degrees.
"Wednesday night looks to be a wet night for most places with extensive hill fog and lowest temperatures of 5 or 6 degrees, with brighter drier conditions following for Thursday in light Southeasterly breezes and temperatures of 8 to 10 degrees.
"Turning cold on Thursday night with some ground frost."
