A Status Yellow snow and ice warning is in effect for counties Galway, Mayo, Clare, Cork, Kerry and Limerick.
A separate Status Yellow warning for the entire country comes into effect from 6pm and will last until midday tomorrow.
Met Éireann is warning of falls of hail, sleet and snow with icy and hazardous conditions.
The Met Office has also issued a Status Yellow snow and ice warning for Antrim, Armagh, Down, Derry, Fermanagh and Tyrone.
AA Roadwatch has said that icy conditions have been reported across the country, while snow is also affecting routes in Donegal, Leitrim, Sligo, Cavan and Monaghan.
? From 6pm this evening a nationwide warning for snow and ice comes into operation. So, after a very cold day - rain, sleet and snow will extend from the West overnight with accumulations of snow.Nuala has the details and further updates @WeatherRTE ??— RTÉ (@rte) January 23, 2021
The Irish Society for the Prevention of Cruelty to Animals (ISPCA) warned animal-owners to take care of their four-legged friends during the cold spell.
"Larger animal including horses and farm animals should be brought inside in a secure stable or shed, so that they are shielded from snow and icy conditions," it said in a statement.
The ISPCA also said pets should be kept safely indoors and advised: "Consider bringing dogs on more frequent, but shorter walks so they spend less time exposed to the cold."
Widespread wintry showers and maximum temperatures of 2C to 4C are expected tomorrow.
There will be frost overnight, but the country will "start to warm up" from Monday.