Derbyshire Armed Response Unit said the people should avoid the area or find an alternative route.
“Any journey at this time should be for essential reasons only.
“If road closure signs appear please don’t ignore them: they are there for a reason,” they said.
Snow is expected to fall throughout the day in Derbyshire as ‘danger to life’ amber warning is in force in East Midlands.
The Met Office said the warning is valid until Wednesday.