The worst of the current wintry weather is behind us, but a severe frost tonight could make roads dangerous, Met Éireann has warned.
Snow and ice over the bank holiday weekend caused difficult driving conditions for motorists in many parts of the country.
The worst of the snow, experienced on Sunday, created particular problems in Cavan, Donegal, Kildare, Kilkenny, Laois, Offaly, Tipperary, Waterford, Westmeath and Monaghan.
There were reports of slippery conditions and black ice on motorways, national routes and roads on high ground.
Parts of the N1, M4, M7 and M9 were badly affected and drivers in north Donegal were advised to travel only if necessary, and to avoid higher ground if possible.
AA Roadwatch also issued a travel alert and strongly advised motorists to continue to take care on all roads.
Some ferry crossings were also cancelled due to the poor weather conditions.
A spokesman for Met Éireann said the country is likely to experience sunny spells and scattered wintry showers today, mainly on western and northern coasts.
Winds will ease and tonight temperatures could drop as low as minus three degrees, causing a severe frost, with icy patches in some areas and possibly freezing fog, again creating difficult and dangerous driving conditions.
Tomorrow the frost, ice and fog will clear gradually and cloud travelling in from the Atlantic will bring outbreaks of rain and milder temperatures by nightfall, the spokesman said.
"We can expect milder weather, with rain and drizzle for the rest of the week," he said.
Temperatures of up to 10 degrees are expected on Thursday and Met Éireann has said Friday will be bright, dry and mostly sunny.