It warned motorists there could be a repeat of the scenes in southern England last week when hundreds of drivers were stranded in their cars overnight.
Darron Burness, the AA's Head of Special Operations, said: "Drivers should be well prepared as even short journeys can quickly turn bad."
He also said snow that settles could persist in the low temperatures, leading to icy patches.
"Wherever you're going, take plenty of warm layers, check the travel reports before heading out and stick to the main roads where possible," he said.
Schools were gearing up to alert parents should conditions force them to close. And county and city emergency teams are on standby to try to keep routes open.
Keith Myatt, communications manager at Arriva, said the company hoped to be able to maintain its services.
He said: "We will regularly monitor our services over the day and over the weekend."
An East Midlands Airport spokeswoman said there was a team on standby in order to deal with the heavy snowfall. She said: "The airport has a contingency plan in place in case the weather does affect operations."
Mr Chivers said: "Over the next couple of days ice will bring problems and will be hazardous. People should prepare for this when they are heading out and about."
But she said the conditions were not necessarily unseasonable. "It's not unusual to get snow in March. It's more common to get snow at Easter than at Christmas. What is perhaps unusual is the length of the cold weather that we have had all the way through February and March."