Forecasters had earlier warned it will be "bitterly cold" for the rest of the week despite a mild day today.
The warning will be in place between 4pm on December 7 until 6pm the following evening.
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The public are also warned to be aware of icy roads and footpaths. North-west winds staying strong and gusty. Frost may linger in places and temperatures at best will range 1 to 3 degrees.
"It will be cold for the next 10 days, with temperatures hardly making it up to 10C during the day", said Mr Eagleton.
Temperatures will drop to zero or below zero tonight for the bulk of the country, he said, but will hit as low at minus 3C in the northwest tomorrow.
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That warning will be in place until midnight.
"The showers will turn increasingly wintry with falls of hail and snow - especially in the north, and a few will push further south this evening".
It is one of three weather warnings now in place around the country. High-sided vehicles and motorcyclists are particularly vulnerable to strong winds.
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In the same week that Met Éireann has predicted snowfall and icy roads in some parts of the country, new research by Liberty Insurance suggests almost three in four Irish drivers (74%) do not feel confident when driving in poor weather conditions.