Temperatures of 4 to 9C are forecast for Monday with one or two showers predicted overnight. Glasgow is expected to drop to -2C, the forecaster said.
Other consequences of very cold weather include temperatures inside hospitals and care homes dropping below the levels recommended for assessing health risks, and challenges for people keeping indoor temperatures at the recommended 18C, the UKHSA said.
Staffing issues, due to travel delays, may also arise from the cold spell.
Between 2 and 11 January, cold northerly winds in Scotland are expected to become dominant across the UK, bringing snow showers mainly to coastal areas that will work south, the Met Office said.
Inland locations across central and southern areas will remain mostly dry but cold.
On Friday, temperatures in the the North East and North West will feel colder due to the wind chill – a temperature of -4C could feel more like -8C, the Met Office said.
The agency also issued less serious yellow cold health alerts for the rest of England, covering the East Midlands, West Midlands, South East, South West, East of England, Yorkshire and the Humber, and London.
Temperatures in areas covered by the yellow warning are expected to fall to around highs of 6C and lows below freezing from New Year’s Day.
Dr Agostinho Sousa, head of extreme events and health protection at UKHSA, said it was “vital” to check in on friends, family and neighbours that are vulnerable
The predicted temperatures can have a “serious impact” on the health of some people, leading to increased risk of heart attacks, strokes and chest infections, particularly for individuals over the age of 65 and those with pre-existing health conditions, he warned.
Cold health alerts and weather warnings were issued for parts of the UK on Christmas Day, forcing several annual open water swimming events to be cancelled.
