Forecasters said: "Showers of hail, sleet and snow will occur in places.
"Snow showers most frequent in Ulster and Connacht and especially so on high ground."
The Weather Advisory is valid from 6pm on Sunday until 3pm on Tuesday.
Weather Advisories are issued by Met Éireann up to about a week ahead to provide early information on potential hazardous weather.
Met Éireann meteorologist Michelle Dillon gave more details of what to expect in her update after the RTÉ news on Saturday.
"There is a change on the way in our weather. It is going to become cold Sunday and for the early days of next week with some wintry showers starting from tomorrow evening. We'll have some frost and ice by night with some bright or sunny spells mixed in between the showers," she said.
The forecaster said rain would clear on Saturday night but it would become much colder as it does. Though cold, she said Sunday would be bright and dry during daylight hours.
Later on Sunday a system would move in along the west coast.
"So, fairly widespread showers, longer spells of rain, hail, some sleet, the risk of thunder and some snow over higher ground in parts of Connacht and Ulster. Some frost and ice to follow into Monday morning and a blustery day with wintry showers of rain, hail and sleet again with some snow over higher ground," she said.
The cold snap will be short lived as it will become milder later on on Tuesday and into the rest of the week but it will remain on unsettled.
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