"Slippery conditions have also been reported around Longford Town, Roscommon Town, Tullamore, Mullingar, Cavan Town, Cork City, Limerick City, Galway City, Portlaoise and Thurles," a spokesperson said.
"Frost and ice are likely on secondary routes and on high ground in particular.
"Remember it takes up to ten times longer to stop on an icy road. In affected areas, slow down, keep further back from the vehicle in front and keep all manoeuvres gentle."
The status yellow weather warning will remain in place until 6pm on Saturday.
Very cold with widespread frost and icy patches this morning and with lying snow in places. All areas will have good sunny spells today and the wintry showers will become more isolated by afternoon. Top temperatures 3 to 5 C., generally, but up to 7 C., on the southwest coast. pic.twitter.com/91pM0jP039
While the wintry showers were previously described as isolated, "serious" snowfall can be expected today and Thursday, according to Met Éireann forecaster John Eagleton.
"The big threat of snow this week is on Wednesday night and during Thursday, as the winds turn easterly in direction and as the pressure to the south of Ireland injects moisture to those easterly winds," he said.
"Once that threat passes, it will remain cold and frosty for Friday and the weekend, and then temperatures will start to creep up again at the start of next week.
The national forecaster predicts that Saturday night will be "bitterly cold" with lowest temperatures of -2 to -7C.