The Met Office issued the update today, which is in effect from 9 p.m. today to 10 a.m. tomorrow.
The new warning applies to a large portion of north and west Kent, including Maidstone, Medway, and Sheerness.
Earlier today, the UK Health Security Agency (UKHSA) and Met Office issued a level two cold weather alert for the south east, which will last until 11.59 p.m. on Thursday.
Light snow is expected in Tunbridge Wells and Sevenoaks, but sleet is expected in many other areas.
Kent County Council (KCC) is urging residents to keep an eye out for vulnerable family members, friends, and neighbours as temperatures in some areas could drop to -3 degrees Celsius.
The local authority predicts widespread frosts, ice, and wintry showers.
Dartford and Dover will see sleet showers on Tuesday and Wednesday instead of snow this week.
And sleet will fall on Medway, Thanet, and Sheppey, despite BBC Weather forecasting a small chance of snow in the area.
Heavy snowfall in December caused havoc across the county, resulting in accidents on several roads.
Temperatures will be below average for this time of year beginning Monday, especially overnight.
“Cold weather can affect anyone,” Kent County Council (KCC) director of public health Dr Anjan Ghosh said. However, the elderly and frail, as well as people with underlying health issues, are more vulnerable to its potential consequences, which range from heart attacks and flu to falls, injuries, and hypothermia.
“That is why it is vital that during this spell of low temperatures, and icy and frosty conditions, people keep themselves and their homes warm – even if this is just by heating the bedroom and living room.
“We also urge residents to look after vulnerable family and neighbours and to assist their local community. Taking steps to stay warm and collaborate with others can make a world of difference.”
Every year, thousands of people die in excess during the winter. Severe cold weather alerts issued jointly by the Met Office and UKHSA elicit responses from the NHS, public health, social care, and other community organisations to assist vulnerable people with health issues.