The organisation's Chief Forecaster said winds will ease as Thursday progresses, but snow showers will become more frequent and heavier.
Met Éireann has also issued weather warnings for wind, snow, and ice on Friday across Ireland.
'At the moment we have a yellow weather warning in place, but it could be upgraded to amber'.
The cold front moves in today and forecasters are predicting strong winds of up to 110km/h in some places, as well as up to 3cm of snow.
Forecasting snow showers in the United Kingdom can be quite challenging as conditions are often borderline between rain and snow.
The yellow level alert is in place from midnight on Friday until 6pm on Saturday.
An North Sea oil rig, off the north-east coast of Scotland, is being partially evacuated over fears extreme waves caused by Caroline could endanger workers.
"Some rural communities could be cut off and power supplies interrupted".
It follows the UK Met Office naming an Atlantic storm which is set to hit Thursday Storm Caroline.
There will be potentially damaging gusts of up to 80mph there, with higher speeds possible across the Northern and Western Isles.
"Road, rail, air and ferry services may be affected, with longer journey times and cancellations possible".
Across the United Kingdom, conditions will start to turn wet and blustery overnight, especially across the North and North West, with strong winds expected early on Thursday.
"There will also be frequent showers across the north and west of the United Kingdom and Ireland through the day, which will turn increasingly to sleet and snow, mainly over high ground".
The Met Office said "predominantly colder periods" are expected through the second half of December until after Christmas, with snow in the Midlands and North.
Snow and falling temperatures are also forecast for parts of Britain later in the week.