"Chilly start to Saturday morning, low single figures for most town and city centres, just below in some rural spots - and that is the theme as we go into the weekend".
Persistent rain will hit the southeast and there will also be frost and some freezing fog.
It said Arctic air would bring frequent wintry showers and snow could settle to 3cm about 100-200m and to 5cm or more above 300m away from the coast.
Met Éireann has warned that wintry showers will give localised accumulations of hail and snow, compacting to ice in some areas and leading to hazardous driving conditions.
The warning covers from 20:00 Monday to 10:00 on Tuesday. "But any showers, and higher ground looks most likely to see them, the Peak District, Snowdonia, the Pennines and of course Scotland". Afternoon highs of 3 and 5 degrees and winds will be fresh to strong southwesterly in the north, light variable in the south.
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She said road users should take extra care, particularly tomorrow morning.
"There will be a rise in temperatures to between 7C and 9C and the night will be frost free".
Snow could also fall in Matlock and Bakewell from 10pm on Saturday, although the Met Office says any snow will quickly turn to rain.
However, forecasters predict there will be a reprieve from Wednesday with unsettled weather bringing warmer conditions and rain.
BBC Weather forecaster Simon King wrote: "There'll be some hill snow from showers over the next few days but perhaps something more significant on Saturday night with a few cm's falling over higher ground of North Midlands, northern England and Scotland".