Status Yellow snow and ice warnings are in place in 11 counties in the north and northeast of the island.
The counties covered by the warning issued by Met Éireann include counties Cavan, Donegal, Monaghan, Leitrim and Sligo.
The warning began at midnight and will last through until midday.
A separate Status Yellow snow and ice warning has also been issued by the UK Met Office across all counties in Northern Ireland for the same time period.
Wintry showers of hail, sleet and snow are forecast with modest snow accumulations expected in places, especially on high ground.
Met Éireann warned of hazardous travelling conditions and icy stretches as possible impacts.
The forecast overall for Ireland is that it will be cold with sunshine and scattered showers, some of the showers will be wintry with hail and sleet.
Some snow showers are possible too, mainly over higher ground in the north and northwest.
Although there will be highest temperatures of 3-7C, it will feel even colder with an added wind chill factor from moderate to fresh north to northwest winds, stronger near exposed coasts.
It comes as temperatures dropped across the country yesterday evening as an arctic airmass begins to move in.
Frost and ice will become widespread for a couple of nights ahead with temperatures reaching as low as -3C in areas later in the week.
Met Éireann meteorologist Rebecca Cantwell warned earlier this week that people should wrap up and give themselves extra time in the morning to defrost their cars.
Speaking on RTÉ Radio One, Ms Cantwell said the average minimum temperature for this time of year is around 3-7C but that maximum temperatures over the next few days will only reach these temperatures and there will also be an added wind chill factor.
There will be some wintry showers of hail and sleet and possibly snow, but these will mostly be over higher ground in Munster and north Connacht, with the east and south expected to be the coldest.
However, by Friday, there should be a return to milder Atlantic air, the meteorologist said.
