The yellow alert initially covered Friday and Saturday but has now been extended to cover a wider area, and also includes Sunday.
Sunday's warning, which covers Derbyshire and Nottinghamshire and is in force between 4am and 11.55pm, states: "A spell of heavy snow is possible over some central parts of the UK during Sunday.
"This could lead to road, rail and air travel delays, with the potential for vehicles to become stranded or public transport to be cancelled.
"Rural communities with limited access routes could become cut off."
Friday and Saturday's warning states that between 10 and 20cm of snow is possible for some locations, including the northwest Midlands.
It adds that icy surfaces are also likely to be an additional hazard.