After snow hit large swathes of the county on Sunday, temperatures dropped to between minus 10 Centigrade and minus 12C overnight in parts of the Midlands and Wales.
The Met Office has issued a yellow warning.
After a frosty and icy start this morning, it will be a fine day with plenty of wintry sunshine and just patchy cloud, mainly this morning. A moderate westerly breeze.
It will be dry tonight with long clear spells and rather cold with a widespread and sharp frost and gentle winds.
Drivers and pedestrians are being warned to watch out for icy roads and pavements. Highways England warned drivers to beware of black ice and to take care.
The Staverton flood gates are closed because of standing water and black ice.
All major roads are currently clear, although the A419 between Swindon and Cricklade has been blocked by an overturned vehicle.
Staff at Kingdown School in Warminster say the school will not be open today for children whose parents are key workers.
Tomorrow, any early brightness will fade away as cloud thickens, giving way to spells of rain in the afternoon. The rain will clear away through the evening. It will be cold with gentle winds.
Wednesday will begin cloudy with the odd brighter spell in places. In the evening, patchy rain and drizzle will spread from the south-west.
The rain will clear early on Thursday, leaving a dry day with sunny spells. Overnight another band of rain will move in from the west.
Friday will turn dry for a time, however, there will be outbreaks of rain later with overcast skies.