Met Eireann have issued a new 24-hour Status Yellow snow and ice warning for 23 counties.
The alert is in place for all of Connacht, Leinster and Munster from 8am on Thursday until 8am on Friday.
It reads: "A band of sleet and snow spreading northeastwards during Thursday giving snow accumulations of up to 5cm in some areas (higher over the mountains), but transitioning to rain in the west and south on Thursday night."
A separate warning remains in place for Louth, Westmeath, Meath, Cavan and Monaghan from 10am on Tuesday until 6pm on Wednesday, with up to 5cm of snow expected.
Meanwhile weather experts are predicting it will stay bitterly cold over the next few days with lows of -5C possible in places tonight.
A Met Eireann forecaster said: "Very cold this morning with icy patches. Today will be blustery with scattered wintry showers of sleet or snow giving some accumulations in places. There will be a mix of cloud with some bright or sunny spells. Highest temperatures of just 1 to 3 degrees, with an added wind chill factor due to fresh and gusty easterly winds.
"Bitterly cold tonight with a widespread sharp to severe frost setting in. Scattered wintry showers will become mainly confined to the eastern half of the country as long clear spells develop. Winds will ease to a light or moderate northeast breeze. Temperatures dropping to between -5 and 0 degrees with icy stretches forming.
"A bright, crisp start Wednesday morning for many areas with lingering frost and ice. It will be very cold again with wintry showers of sleet or snow mainly affecting north Leinster, east Ulster and the midlands. Many areas elsewhere will stay dry with sunny spells. Highest temperatures of 1 to 3 degrees at best, with a moderate easterly breeze.
"Largely dry, cold night on Wednesday with isolated wintry showers and clear spells. However rain, sleet and snow will move into the southwest overnight as southeasterly breezes freshen. Winds will become strong and gusty across the southwest. Lowest temperatures of -4 to +1 degrees with frost and ice forming, coldest in Ulster."
And Thursday will see "hazardous" conditions as snow is set to move across the country, before temperatures plummet to -1C.
While further snow could arrive for Ulster and north Leinster on Saturday, with lows of 0C overnight.
A forecaster added: "Sleet and snow will slowly extend northwards from the southwest, with snow accumulations leading to hazardous conditions. Highest temperatures of 1 to 3 degrees. Feeling colder in fresh and gusty southeast winds, strongest in western and southwestern counties.
"Remaining breezy overnight with sleet and snow continuing to fall over much of the east, midlands and north leading to further accumulations. However, precipitation will turn to rain in parts of the south and west. Lowest temperatures of -1 to +2 degrees with fresh southeasterly winds.
"Sleet and snow may linger for a time in the eastern half of the country on Friday, with outbreaks of rain elsewhere. Becoming drier in the afternoon before rain develops in the west in the evening.
"Southeast breezes will strengthen during the day, becoming strong and gusty in coastal counties. Highest temperatures generally of 1 to 4 degrees, however less cold in southwestern counties with highs of 5 to 8 degrees.
"Windy with outbreaks of rain on Saturday, possibly continuing to fall as sleet and snow in Ulster and north Leinster for a time. Southeast winds will be fresh to strong and gusty.
"Remaining cold across the north, east and midlands with highest afternoon temperatures of 1 to 5 degrees, a few degrees milder elsewhere. Windy overnight with outbreaks of rain continuing with some wintry falls possible in parts of the north and east. Lowest temperatures of 0 to 4 degrees, with milder conditions persisting in the southwest.
"Current indications suggest Sunday will remain unsettled with breezy conditions and further rainfall. Some uncertainty regarding temperatures, with a possibility of colder and wintry conditions persisting in the eastern half of the country."
