The risk of hail and thunder will also increase towards morning.
Met Éireann has issued several weather warnings ahead of the arrival of Storm Gareth this week.
According to the status yellow warning, winds will reach mean speeds of 50 to 65km/h and gusts of 90 to 110km.
"Wintry showers will also continue through Sunday evening and night onwards into Monday morning, especially over Scotland and Northern Ireland", a Met Office spokesperson said.
The rest of the country will remain under a yellow wind warning until 6am on Wednesaday.
Storm Gareth is expected to hit the United Kingdom on Tuesday, bringing wind speeds up to 80mph and heavy rain.
The storm, which follows last month's Storm Freya, was named by the Irish Meteorological Service and will bring strong winds and heavy rain to the United Kingdom on Tuesday and into Wednesday.
The Met Office's Paul Gundersen said: "The strong north-westerly winds will also affect southwest Scotland late on Tuesday, spreading across much of England and Wales through Wednesday". Highest temperatures of 4 to 8 degrees with fresh, gusty westerly winds, strong in coastal areas.
Those western counties can expect storm force winds reaching average speeds of 65-75km/hr, and gusts reaching 130km/hr.
The heavy rain is expected to arrive in Penzance at around 7pm this evening, easing off around 11pm, as it sweeps eastwards - arriving in Plymouth at around 9pm.
Very strong winds are forecast from mid-afternoon and over the course of a full 24-hour period.