The warning states: "During Friday, increasingly frequent snow showers already affecting parts of Scotland, Northern Ireland and northern England will extend across many other northern and western parts of the UK.
"2-5 cm of snow is likely fairly widely, with 10-20 cm in places, mainly northern Scotland, Northern Ireland, north Wales and perhaps the northwest Midlands. Icy surfaces are also likely to be an additional hazard, especially overnight."
The warning for snow and ice is in place from Friday (December 8) and covers Bradford, Huddersfield, parts of Wakefield and a little of West Leeds.
It also covers Sheffield and parts of South Yorkshire.
Here is the general forecast for the coming days:
Persistent moderate to heavy rain will continue to spread south-eastwards, from Ireland and western Britain, reaching the south-east by dawn.
Moderate to fresh south-westerly winds, strong to gale force in exposed areas with gusts over 50mph for exposed headlands.
Behind, Ireland will become dry and partly cloudy, with winds veering to north-westerlies feeding frequent snow showers into western Scotland, rain showers nearer the coast.
The winds over Scotland will be gale force with gusts 50-60mph. Minimum temperatures will be 1 to 4C in the Highlands, 5 to 9C elsewhere in Scotland and Ireland, and 8 to 10C in England and Wales.
Predicted weather patterns for Thursday afternoon
(The Weather Company)
A very unsettled day as Storm Caroline passes eastwards. Overnight heavy and persistent cold front rain spreading to central and southeast England but this will clear to the near-continent.
Turning much colder in clearance of that front with heavy snow over the Scottish Highlands and gales with blizzard conditions.
Gusts will be over 70mph but greater than 80mph for parts of north-east Scotland with frequent and blustery wintry showers.
Some of those showers will feed through the Cheshire gap to the Midlands. Maximum temperatures will be above average, 6 to 8C in Scotland and Ireland, 10 to 13C in England and Wales, locally 14C in the south-east.
A very cold and blustery day with frequent snow showers moving into coastal areas on a brisk northerly Arctic breeze.
Some of those showers will edge further inland, even reaching the Midlands, through the Cheshire Gap, giving snow to lower levels.
Snowfall totals expected to be 2 to 5cm over higher ground of Wales, northern England, Scotland and Ireland, locally 10cm in the far north.
In between the showers it will be a cold yet sunny day.
Gale force northerly winds over northern areas, moderating further south and inland. Maximum temperatures as low as -3C in the Highlands, 2 to 4C widely, 3 to 5C in the south and 6C on the Cornish Peninsula and the far south-west of Ireland.