Forecasters are predicting that the current "changeable and unsettled" weather will last until at least the weekend.
A Status Orange fog warning was issued by Met Eireann last night.
This morning is expected to be dull and misty with patches of light rain and drizzle as the fog clears.
But it will become mainly dry during the day, with bright or sunny spells developing and maximum temperatures 9 or 10C.
It will be dry overnight with clear spells although a few patches of mist and fog may develop.
Tomorrow will be dry and bright although it will be cool, with top temperatures of 8 to 10C.
The forecaster say the mainly dry conditions will last until Saturday at least but it will gradually turn cooler as the week goes on.
Night will be cold with a risk of frost and mist and fog patches are likely on Wednesday.
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Looking ahead to the weekend, Met Eireann say: "Mainly dry, settled conditions continuing, with bright or sunny spells at times and just a small chance of a few isolated light showers, especially in the western half of the country.
"Winds will be mostly moderate southeasterly, but it will become windy along Atlantic coasts by Saturday, with fresh to strong southeasterly winds developing there.
"Maximum temperatures on Friday 10 to 13 Celsius, but Saturday will be colder, with maximum values of 8 to 10 degrees.
"Nights will be cool, with minimum temperatures of 1 to 5 Celsius, but frost is unlikely.
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"Sunday: There is still some uncertainty, but current indications suggest that it will remain dry and bright in most areas, but rain may develop in the southwest, and, later in the day, possibly also in western parts of Connacht.
"Quite a cold day, in moderate to fresh southeasterly winds. Max. 7 to 10 C."
The further outlook is uncertain, with early indications suggesting it will be more changeable and unsettled.
