Met Eireann has issued an official snow and ice warning for 10 counties.
The Status Yellow caution is in place from 12.01am tomorrow until 12pm on Wednesday.
The counties included in the warning are Galway, Mayo, Sligo, Roscommon, Leitrim, Cavan, Monaghan, Donegal, Longford and Louth.
It comes after forecasters warned temperatures were going to plummet overnight.
A spokesperson said: "Tuesday will be a cold, blustery day, with sunny spells and showers, the showers mainly in the western half of the country in the morning, but becoming widespread during the day.
"Some of the showers will be heavy and of hail, with wintry showers of sleet possible also. There is a risk of snow showers over mountains and also a risk of thunder.
"Maximum temperatures 5 to 9 Celsius, in mostly moderate to fresh and gusty west to northwest winds."
Tuesday night will be a bitterly cold and frosty night as temperatures drop to as low as 0C again.
A Met Eireann spokesperson added: "Cold, with further showers, some wintry.
"Most of the showers will be in Atlantic coastal counties, but they will occur in other parts also, especially in parts of the east and southeast.
"However, many areas will be dry, with clear spells. Minimum temperatures 0 to 4 Celsius, with a risk of frost in places sheltered from a moderate north to northwest wind. The risk of frost is greatest in the east."
The cold conditions and risk of thunder will continue into Wednesday, Thursday and Friday.
There will still the possibility of wintry showers as temperatures remain below average for the time of year.
"Cold, with a mix of sunny spells and showers, some heavy and of hail, with a continuing risk of thunder.
"Some of the showers may be wintry also, especially over high ground.
Irish weather forecast: Met Eireann warn of 'severe frost' as temperatures plummet this weekend
"At night, good clear spells will develop, with most of the showers retreating to western, northern and eastern coastal counties.
"Temperatures will be two or three degrees below normal, with typical maximum values of 6 to 10 Celsius. Overnight lows will range 0 to 4 Celsius, possibly a little lower in some parts, with a risk of frost.
"Wednesday will be quite windy, with moderate to fresh north to northwest winds, strong along Ulster, Connacht and west Munster coasts.
"Winds on Thursday will be mostly moderate north to northeasterly, decreasing further on Friday, becoming light to moderate easterly or variable by then.
"A few mist or fog patches may occur on Thursday and Friday nights, with lighter winds."
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