Road users are being urged to drive with care as temperatures are set to drop as low as -5C or -6C in some parts of the country overnight.
A Status Yellow warning for low temperatures and ice is in effect for Cavan, Donegal, Monaghan, Connacht, Longford, Louth, Meath and Westmeath until 9am tomorrow.
Met Éireann warns of harzardous conditions with icy stretches on roads and footpaths.
A separate Status Yellow warning for snow and ice will come into effect at midnight for Cork and Kerry, and will remain in place until midday tomorrow, with patchy sleet or snow overnight bringing the potential for hazardous conditions on some roads and footpaths.
A Status Yellow warning for snow and ice for counties Antrim, Down, Tyrone and Derry - issued by the UK Met Office - is in place until 9am tomorrow.
Met Éireann forecaster Joanna Donnelly said there would not be anything in terms of snow accumulation until Thursday, but she warned that anticipated snowfall could end up falling as sleet.
"It's always on a fine point because we're on the edge of the cold air," she said.
"We're on the edge of the milder air from the Atlantic, so it's always very, very fine between whether it's going to turn to sleet or turn to snow.
"At the moment, it looks like it might snow on Thursday."
Speaking on RTÉ's Today with Claire Byrne, Ms Donnelly said it looks as though conditions will remain cold until at least the weekend.
She said all surfaces would be "tricky" over the coming days because any precipitation will freeze.
"Paths, footpaths, cycle lanes, road surfaces - they're all going to be tricky," she said.
"You need to really watch where you're going, no matter where you're going or how you're getting there".
Wednesday will start cold & frosty🥶, especially over the northern half of the country with some icy stretches❄️. Sunny spells will develop⛅️.— Met Éireann (@MetEireann) March 7, 2023
Cloudier further south with patchy rain🌧️, sleet & snow🌨️.
Highs🌡️ of 3 to 6°C with light/mod easterly winds🍃, fresher in the SW. pic.twitter.com/BCZrdzpcme
The head of communications with the Road Safety Authority also urged road users to exercise caution as the colder weather has brought about a change in conditions.
Speaking on the same programme, Brian Farrell said it is important to anticipate all the risks on the road, with a particular risk of ice and black ice this morning.
"This comes on the back of a mild spell. And it is a change in conditions and we really have to get our mind in gear for some more winter driving this week," he said.