There's a chance of snow in parts of Leinster and Munster later this week
Met Éireann says there's a very cold week in store, and that temperatures on Wednesday won't get above freezing.
A status yellow ice warning is in effect for Antrim, Armagh, Down and Derry until tomorrow morning.
In the Republic, very cold conditions are expected right through to Friday.
Temperatures could fall as low as -3 degrees in parts of the country tonight and tomorrow night.
Meteorologist Paul Downes says today's wintry showers may worsen as the week goes on.
He said: "Tonight and tomorrow, [rain and sleet] may turn over to snow - especially if they drift inland into Leinster and part of Munster... around higher ground.
"On Wednesday, another bitterly cold day... temperatures will probably not get above freezing in some areas.
"Another band of sleet or snow will cross the country on Wednesday night into Thursday, with possibly some accumulations."
He added it will remain cold with some wintry showers for the rest of the week.