Top temperatures in some areas at the weekend will be around 1° C to 2° C in the north and east of the country, while it will be milder in west and south west coasts with highs of 5° C to 6° C.
There had been observations that the Beast From the East could make his presence felt on St Patrick's Day.
Rain in northern areas will slowly clear during Thursday morning but elsewhere will be a brighter and drier day with showery rain affecting mainly the south and west.
Met Eireann's Liz Gavin says "very cold conditions will extend across the country on Saturday and Sunday".
"Some of the showers will be of rain or sleet, but some snow showers will occur also", Met Eireann said.
"It will be breezy with easterly winds".
Remaining very cold on Sunday, with scattered snow showers, majority in Leinster and the eastern half of Munster, but well scattered elsewhere, with sunny spells.
"On Friday, temperatures will range from freezing zero degrees Celsius to four degrees Celsius. Very cold and frosty again on Sunday night, but mostly dry".