South West Trains said it was running a revised timetable throughout its network because of the snow, and would be concentrating on its mainline services.
The company said there would be no services between Ascot in Berkshire and Ash Vale in Surrey, between Virginia Water and Weybridge, or from Salisbury to Bristol.
It was also running revised timetables on other routes.
Southern said trains were unable to operate between Lewes and Haywards Heath in Sussex or between Horsham and Dorking or Reigate and Redhill in Surrey.
The Southern service between South Croydon and Milton Keynes was also suspended.
More top news
The Prince of Wales' household is so riddled with infighting it is nicknamed Wolf Hall, according to a new unofficial autobiography.
There will be blustery showers across northern parts overnight with showery rain and sleet across the south.
Rap mogul Marion 'Suge' Knight has been arrested on murder charges after a fatal hit-and-run incident in Los Angeles.