The yellow ‘be alert’ warning kicks in from midnight on Sunday until midday on Monday and there could be “significant accumulations”.
The Met Office said: “Heavy snow on Sunday and overnight into Monday may cause some disruption.”
The forecaster added: “There is a small chance that power cuts will occur and other services, such as mobile phone coverage, may be affected.
“There is a slight chance that some rural communities could become cut off.
There is a chance of travel delays on roads with some stranded vehicles and passengers, along with delayed or cancelled rail and air travel.”
The weather warning covers much of the UK.
The Met Office added: “Whilst not all areas may be affected, outbreaks of snow will likely develop during Sunday and Sunday night, potentially giving some significant accumulations in places.
“The greatest risk is in southern and eastern Scotland, where 2-5cm may accumulate in quite a few places and perhaps as much as 10-20 cm over high ground.
“Rain or sleet is more likely near some northern and eastern coasts.”