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 German bomb - a 500kg device - was spotted by a barge carrying out dredging works, the Royal Navy said.
The study found children born in the 1980s have found it much harder to build up wealth in housing and pensions as they age.
The singer ended speculation over who would perform by saying "the rumors are true" to her 63 million Twitter followers on Friday morning.