South Downs Park officials say that snow could start falling from around 12 noon on Saturday until Sunday evening.
And, they say, there is a chance of more snow on Monday (February 8).
The Met Office has issued a warning of ‘severe cold weather’ across Sussex with a strong easterly wind leading to icy road conditions.
A spokesman said: “There is a risk of snow in the far southeast on Saturday night into Sunday morning.”
He added: “All parts of England may be going into a more notable cold spell of weather as we head into the coming week with sharp overnight frosts and temperatures near freezing by day.”