The kit should include an ice scraper, a warm jacket, boots, jump leads, a shovel, a torch, a warm drink, a snack, a first aid kit and a warning triangle.
The service tweeted: "As the #badweather continues please #takecare when travelling as roads and pavements may be slippery.
"If you are going on a journey in the car please ensure you have these items in case of an emergency."
The Met Office has issued an amber weather warning has been issued for snow across South Yorkshire.
Fierce Siberian winds could lead to blizzard conditions and drifting of snow with up to six inches of snow falling in places.
The warning - which is in effect between 4pm today until 9am Sunday - states: "Snow showers are expected to become more frequent through Saturday evening and night with icy patches also developing on some untreated roads, pavements and cycle paths.
"Strong easterly winds will lead to some temporary blizzard conditions and drifting of snow.
"Travel delays on roads are likely, stranding some vehicles and passengers. Some delays and cancellations to rail and air travel are likely.
"There is a chance that some rural communities will be cut off. Some injuries from slips and falls on icy surfaces are expected."