The Met Office says snow, possibly heavy at times, will develop overnight tomorrow (Tuesday) and into Wednesday, and warns that there is a small chance of travel delays. The warning affects most of central and eastern England, including the West Midlands.
Temperatures are also expected to fall once more, with further snow possible later in the week.
Councillor Hazel Malcolm, the City of Wolverhampton Council's Cabinet Member for Public Health and Wellbeing said: "When the mercury in the thermometer is plunging, it's important that people keep an eye on the weather forecast and plan the day around it.
"People should take extra care when they are out and about, dress warmly and wear non slip shoes to limit any falls, and make sure they stay warm when they are indoors, particularly if they're aged 65 or over, or have long term health conditions.
"Homes should be kept at a minimum of 18 degrees centigrade, and wearing lots of thin layers and eating hot food will help people stay warm.
"I'd also urge people to look out for friends and neighbours who may be vulnerable to the cold. Please make sure they have access to warm food and drinks, have sufficient stocks of any medicines they may be on, and are managing to heat their homes adequately."
Stay Well This Winter contains useful advice on staying warm and keeping healthy during the cold weather.
The Met Office forecast for Wolverhampton can be found at Met Office.