The Met Office said some slight snowfalls are likely today, with 1 to 2 cm of fresh snow in a few places, but overall the focus switches to ice, with temperatures staying below zero over snow cover for many areas.
A spokesman said: "The public should be aware of the risk of localised disruption to transport during this spell of wintry weather."
Steve Crosthwaite, head of the Highways Agency's National Traffic Operations Centre, said: "We advise drivers to check road conditions and the Met Office weather forecast before they set off and during severe weather to consider whether their journey is essential. They may want to delay their travel until conditions improve and to allow our winter fleet the chance to treat the roads.
"Our traffic officers are working round the clock to monitor the network, deal with any incidents and keep traffic moving."
In Wiltshire bus company Faresavers is attempting to run as full a service as possible, but has announced the following ammendments.
The X31 will operate full route except for Leafy Lane which is quite icy at the moment.
The X72 will operate full service except for Kingsdown and Bathford, divert through Box.
The 228 will operate with exception of the Barracks and Pinewood. Colerne crossroads will be served.
The 635 will operate with exception of Withymead end of Marshfield, and Chesley/Naishcombe hill in Wick. Marshfield High St ok.
There will be no 95 service between Brinkworth and Chippenham. The 99 service will operate between Chippenham and Kington St Michael. Chippenham Town services are going to attempt to service all routes with exception of top of Barrow Green. Greenway Lane Co-op should be ok.
The 87, 77 and 85 services are out running but may only be able to service main roads.