The Met Office has issued a yellow weather warning for snow that covers the whole of Richmondshire.
The warning comes into force at 3am on Friday and lasts until 12noon the same day.
Forecasters say areas to the east of the Pennines could see accumulations on lower ground as well as the hills.
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The chief forecaster said a band of rain, heavy at times, was expected to move eastwards over the UK.
They added: “With cold air in place, a spell of snow looks likely to develop on its eastern edge.
“Above around 100 metres, 2-5 cm is possible quite widely, and up to 10cm over higher ground.
“Some places to the east of the Pennines may see some accumulating snow to lower levels.”
The snow is predicted to ease on Friday afternoon.
Temperatures will remain at around 0C.
