Ice was initially predicted across the country but experts dropped that prediction in favour of snow being the primary risk.
The warning covers south west Scotland, the Lothians, Grampian, Highland, Strathclyde, Central, Tayside and Fife.
Heavy snow will "at times bring some travel disruption", the Met Office said, leading to travel delays, possible cancellations to rail and air services, power and phone interruptions and the possibility that some rural communities may become cut off.
Temperatures across the central belt are forecast to remain low today, rising from freezing to 1°C, but experts have forecast that it is expected to feel more like -5°C or -6°C.
Similarly, the north east of Scotland is expected to see temperatures close to freezing today but the Met Office has said that it will feel like -4°C or -5°C.
Forecasters are warning of a strong chance of roads becoming blocked by deep snow, "with many stranded vehicles and passengers likely". Snow accumulations of 5-10 centimetres will be widespread in the affected area, and reaching up to 30cm in "a few sites".
A statement on the Met Office website said: “Snow showers will feed off the North Sea into many northern and eastern areas of the UK.
“Some icy stretches are possible overnight, mainly where melting snow during the afternoon has not a chance to dry out before freezing overnight, although snow is likely to be more prevalent.”