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 outspoken Birmingham MP tweeted a picture of locksmiths ramping up security at her home after facing fresh intimidation on social media.
Islamic State's Amaq news agency released footage showing French attacker Abdel-Malik Nabir Petitjean urging Muslims to destroy the country.
Brighter skies developing across northern Britain and Northern Ireland with some sunshine tomorrow but feeling cooler again.