Snow and ice are being forecast in each county from tonight.
Met Éireann has issued a status yellow warning for the country, saying icy and slippery conditions are expected due to an accumulation of ice and snow on untreated surfaces.
The warning is in place from 9pm tonight until 7pm tomorrow evening.
The forecaster says scattered sleet and snow showers will be most frequent across Ulster and Connacht.
There will be some showers in central and eastern areas at times, with the odd flurry further south.
Between 1cm and 2cm of snow is expected to fall.
Wintry showers will be confined to northern areas by late Tuesday evening.
It will be cold through much of this week with frost, icy patches and some wintry precipitation at times.
Temperatures are expected to increase Thursday into Friday, before turning colder again.
Met Éireann expects colder weather over the weekend.
"Current indications suggest it will becoming colder again this coming weekend, but still some uncertainty as to the exact detail as of yet."