The Met Office yellow alert is valid between midnight and noon on Tuesday.
A Met Office spokesperson said: "A band of rain and hill snow will move southeastwards across the UK during Monday evening and overnight.
"A brief spell of wet snow is possible on high ground of southern Scotland, northern England and north Wales, with some small accumulations possible.
"Behind this, surface temperatures will rapidly fall away with some ice forming on some surfaces.
"Once the rain has cleared, some hail, sleet and snow showers will follow from the northwest, with one to three centimetres above 200 metres and some small accumulations expected at lower levels."