The amber ‘be prepared’ alert is for between 2am and noon tomorrow (Tuesday February 27).
It covers the north of the county, and parts of West and East Sussex.
Those areas not covered are still on a yellow ‘be aware’ alert.
The Met Office says: “Snow showers or longer periods of snow are expected on Tuesday, accompanied by very low temperatures.
“There is the likelihood of travel delays on roads, with some stranded vehicles and passengers, as well as delays or cancellations to rail and air travel.
“Some rural communities could become cut off. Power cuts may also occur and other services, such as mobile phones, may be affected.”
The Chief Forecaster’s assessment is: “Further snow showers are expected through Tuesday, these likely to be heavy in places and probably aligned in bands.
“Where this happens, there is the potential for 5-10cm of powdery snow accumulating, possibly very locally 15cm, through the morning, before easing during the afternoon. Meanwhile some nearby locations may see only small accumulations of 1-3cm.”