The Met Office has issued a snow and ice warning for Cumbria from tomorrow.
An area of rain pushing north-eastwards is expected to turn snow in places as it encounters colder air across Scotland and parts of northern England.
At first the main hazard may be of rain falling onto frozen surfaces leading to ice, especially on higher level routes, the Met Office said.
Snow will become more likely later tomorrow and for a time on Thursday.
Heavier snowfall is more likely above 200m in England, where 5cm to 10cm of snow may accumulate, possibly 20cm on highest routes.
At lower levels, 2cm to 5cm of snow may accumulate in places.
The Met Office said the situation remained finely balanced, with the possibility that most lower-lying areas in northern England see rain or sleet rather than snow.