The weather warning was issued shortly after 2pm on Tuesday.
The yellow level alert is in place from midnight on Friday until 6pm on Saturday.
The warning was issued at around the same time Storm Caroline was officially named by the Met Office in the United Kingdom.
Loss of power will be another concern, along with large waves at the coast.
An operation to take around 70 oil rig workers off the Ninian Southern platform, operated by CNR International, is under way.
Kent is set for an Arctic blast of snow as temperatures plummet, according to the Met Office.
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Weather satellite imagery depicts the storm heading westward.
Met Office predictions don't now show snow for London on Monday as their forecast doesn't quite go that far.
Sunday's weather warning is in force from 04.00 on Sunday until 23:55.
'Overnight, the main feature will be the increase in wind as Caroline starts to come in towards the end of the night.
Met Office meteorologist Marco Petagna said: 'Wednesday will see the last of the mild days, with temperatures in double figures, between 10 and 12 degrees (50F-54F).
Severe gales and snow showers have caused travel disruption, school closures and power cuts as Storm Caroline sweeps in to the UK.
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Freezing temperatures are then forecast for parts of Britain on Friday, with a yellow snow and ice warning in place for Scotland, Northern Ireland, western England and Wales.
There will be potentially damaging gusts of up to 80mph there, with higher speeds possible across the Northern and Western Isles.
Rail passengers have also faced disruption, with trains cancelled after a trampoline blew onto the line in East Renfrewshire and services suspended elsewhere.
Britain faces a -16C shiver from Siberia - as a colder-than-normal December was predicted by the Met Office winter forecast.
As Caroline clears, the winds will swing round to the north, bringing colder air and the return to more wintry conditions.
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