Temperatures will drop to as low as -3 degrees on Tuesday night, but conditions will turn milder as the week goes on.
Today (Tuesday November 26) will see highs of 5 to 9 degrees, while temperatures could drop below 0 in parts of the country overnight.
A Met Eireann forecaster said: "Largely dry and sunny in most areas today apart from some well scattered showers, most likely in coastal parts of the north, west and south. Cloud will build in the south and southeast later this evening with heavy showers or longer spells of rain developing. Highest temperatures of 5 to 9 degrees with light variable breezes.
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"Showery rain will continue in the southeast and east with a few coastal showers in the north, otherwise it'll be dry tonight with frost and patches of mist and fog developing in many areas. Lowest temperatures of -3 to +2 degrees in mostly light variable breezes."
Tomorrow (Wednesday November 27) will be mainly dry, but chilly too with daytime temperatures ranging between 3 and 7 degrees and overnight dropping to -2 to +2 degrees.
Met.ie says: "Areas of mist and fog will be slow to clear through Wednesday and may linger all day in some parts of Munster. There'll be some showers at first especially in the east with a few isolated showers too near the north and northwest coast, otherwise it will be a largely dry day with some spells of sunshine. A chilly day with highest temperatures of 3 to 7 degrees, colder where fog lingers, in mostly light northerly or variable breezes.
"Cold and dry Wednesday night with frost and icy patches developing. Mist and fog will form in light winds early on before winds freshen in the west through the night. Cloud and rain developing in the southwest towards morning. Lowest temperatures of -2 to +2 degrees."
The national forecaster says the weather will turn "milder and a little more unsettled as we move towards the end of the week."
Thursday (November 28) will be cloudy and mainly dry, with some scattered outbreaks of rain in parts of the country. It will be much milder both during the day and at night.
Met Eireann's forecast reads: "Cloud, rain and drizzle will spread from the southwest through the morning but staying largely dry with some sunny spells towards the north and east. Cloud will build elsewhere through the day and it'll become breezy. While there'll be some further scattered outbreaks of rain and drizzle in the west and south, it'll hold mainly dry elsewhere. Highest temperatures of 9 to 13 degrees with southeasterly winds increasing mostly fresh and gusty, stronger in some coastal parts.
"Cloudy and breezy Thursday night, with outbreaks of rain and drizzle, mainly over the western half of the country. Lowest temperatures of 5 to 10 degrees in moderate to fresh and gusty southeasterly winds."