Met Eireann has said temperatures for the first half of next week will remain well below normal, although not as severe as the recent Arctic spell.
Forecasters are predicting dry weather until Wednesday, with highest daytime temperatures of four to five degrees.
Snow showers are expected in Northern areas next Friday, although details for the second half of the weekend remain uncertain.
The AA is warning that many roads around the country remain treacherous, while the Conor Pass in Kerry and the Wicklow and Sally Gaps remain closed.
Anne O'Donnell, from AA Roadwatch, said drivers need to be on the alert for ice, black ice and frozen slush.