Met Éireann has warned that up to 8cm of snow may fall in parts of the country.
Issuing a Status Orange Snow-ice warning for Connacht, Cavan, Monaghan, Donegal, Clare, Kerry and Limerick, the agency warned of "wintry, thundery showers of hail, sleet and snow along with icy patches on roads and footpaths" from the early hours of tomorrow until Wednesday morning.
It added that there could be snow accumulations of 4-8cm.
"The highest amounts will be on high ground in Connacht and west Ulster", it said.
A Status Yellow warning was issued for Leinster, Cork, Tipperary and Waterford.
Met Éireann warned of "wintry showers of hail, sleet and snow along with icy patches on roads and footpaths... with snow accumulations of up to 4cm in places".
Earlier today, an ESB spokesperson said that power outages due to bad weather were no longer a problem across the country, reporting a "normal day".
The spokesperson also said an outage which affected 4,000 homes in Greystones, Co Wicklow, was due to a cable fault, not bad weather.
An Aer Lingus regional flight, operated by Stobart Air from Dublin to Leeds Bradford Airport, was cancelled this morning due to high winds in Yorkshire.
A spokesman for Irish Ferries said that sailings of its fast ferry service between Dublin and Holyhead had been cancelled today due to the weather.
However, the conventional ferry service was still operating as normal.
An early-morning sailing between Rosslare and Pembroke was cancelled.