Rain or sleet is more likely near some northern and eastern coasts.
The forecaster said the conditions could lead to power cuts and travel delays.
Friday’s Scottish Championship fixture between Airdrieonians and Falkirk was postponed because of a frozen pitch in Airdrie.
Saturday’s League Two games at Elgin and Peterhead have also been called off, with pitch inspections due at several other fixtures across the country.
Forecasters said temperatures could drop as low as -10C in parts of rural Scotland overnight.
A yellow warning for snow covering much of the central belt on Sunday was removed by Met Office forecasters.
A more severe amber warning for snow is in place just south of the border between 21:00 on Saturday and midnight on Sunday.
The Met Office said it could lead to sever disruption, including power cuts, road delays, travel cancellations and rural communities being cut off.