According to the status yellow warning, Connaught and Ulster will see the heaviest snowfall, but all counties will be affected.
The Met Eireann weather alert is valid from midnight on Saturday night for a total of 24 hours.
Motorists have been advised to watch out for slippery roads due to an accumulation of frost and ice overnight, as temperatures are set to drop to -2 degrees.
Two other yellow alerts warn of strong winds as strong as 110km/h and heavy rainfall across the country.
The yellow wind warning – which is in place for Munster, Leinster and Galway – comes into effect at 3pm on Saturday until 8pm.
Met Eireann also warn of gale force winds on the Irish Sea over the course of Saturday morning.
Connacht, Cavan, Monaghan and Donegal fall under the yellow rainfall warning as accumulations of up to 35mm expected.
There is a risk of spot flooding early morning and the warning remains in place until midnight Saturday.
While Saturday temperatures could reach 12 degrees, Sunday is forecast to be very cold with sunny spells and showers of rain, sleet and snow and a risk of thunder.
Daytime temperatures will reach just 2 to 6 degrees tomorrow with fresh west to northwest winds, according to Met Eireann.
The cold snap will continue into Monday with wintry showers overnight and frost and ice developing. Temperatures are expected to plummet to -3 degrees.
Tuesday will have scattered showers and will continue to develop frost and ice into Wednesday morning.
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