Met Eireann have issued a Status Yellow snow and ice warning for all of Ireland.
A Yellow wind warning has also been issued by the national forecaster, with gusts of 110km/h expected.
The snow and ice warning will take effect from midnight on Monday and will remain in place until 11.59pm on Tuesday.
It reads: "Widespread wintry showers on Monday and Tuesday with some snowfall accumulations, especially in the west and north. Some disruption to travel is possible, particularly over higher routes."
And the second alert is a wind warning for the entire country, with gusts of up to 110km/h expected.
The warning began at 12 noon on Sunday and will stay in place until 12 noon on Monday.
It reads: "Storm Ciara will continue to produce very strong west to southwest winds over Ireland with mean speeds of 50-65km/h and gusts generally of between 90 and 110km/h, higher in Atlantic coastal areas."
The earliest snowfall could hit tonight as temperatures fall close to freezing in many parts of the country.
A Met Eireann forecaster said: "Windy this evening and tonight with stormy conditions returning to some Atlantic coasts. Much colder with showers turning wintry and giving falls of sleet and snow.
"Some snow lying by morning especially over hills in the North and West. Overnight lows of 1C to 3C."
More strong winds, and more snow, are also expected tomorrow, and the heaviest snowfall is likely on Monday and Tuesday.
A forecaster added: "Tomorrow will be bitterly cold and very windy again with a significant wind chill factor and the likelihood of stormy conditions along Western and Northern coastal areas.
"Very showery too, wintry at times, with hail, sleet and snow but sunny spells also. Highs of only 4 to 6 degrees.
"Very cold and very windy on Monday night with strong to gale force West to Northwest winds, severe winds possible near Western and Northern coasts.
"Further hail, sleet and snow showers feeding in with further accumulations of snow in parts and icy patches. Lows around freezing.
"Tuesday will be a bitterly cold day and still very windy with a significant wind chill factor. Very showery too, still wintry at times, with hail, sleet and snow.
"Westerly winds will be fresh to strong and gusty, with gales in western and northern coastal areas. Highs of only 3C to 7C.
"Winds moderating overnight with some frost and ice developing too, and overnight lows of -1 to 2 degrees."
