2.52pm UPDATE: Conditions on the Bath area's roads eased slightly this afternoon after a morning of travel chaos.
Police were still urging drivers to think twice about taking to the roads as bus services were resumed in some parts of the city.
Virtually every school in the area was closed after snow began falling in the early hours.
Only Chandag Junior, St Andrew's and Widcombe Infants were open in the state sector, with Monkton Combe also open.
The snow began easing this lunchtime and council chiefs said the outlook was for a slow improvement.
B&NES said: "We are not expecting any heavy smow but light flurries may still persist. The situation is becoming increasingly positive."
One of the biggest problem areas was Brassknocker Hill which B&NES said continued to be impassable, although gritters are there.
A stuck vehicle on Dunkerton Hill has been cleared and the road is passable with care.
A crash on the A37 at Whitchurch and problems on the same road at Farrington Gurney have also been cleared and the stretches are passable with care, as is the M4, the eastbound carriageway of which was shut earlier this morning between Bath and Bristol.
But the council added: "With road temperatures hovering around freezing, road conditions are particularly difficult and drivers are asked to take great care, especially when passing cyclists."
Bus operator First this morning took all its vehicles off the road, including park and ride services, while B&NES Council suspended its rubbish collections.
Council chiefs urged people to take great care, saying that “steep hills are very difficult and disruption is inevitable.”
Karen Baxter, spokesman for First Group, said: “The message is we are absolutely trying to do our level best to get people out. Buses this morning were taking three and a half hours to a journey that should take 20 minutes. Vehicles were also slipping all over the roads that’s why the decision was taken to suspend services to make sure the journey is safe for our drivers, customers and other road users.”
Bus services began restarting in some areas this afternoon.
Avon and Somerset Police, which at one point was dealing with 20 crashes across the force area, said: "We're advising motorists, in particular heavy goods vehicles, to avoid making journeys unless they are absolutely necessary.
"Around 10-15cm of snow is expected to have fallen by the end of today, making highways dangerous for driving.
"While there have been no major incidents on the roads in Avon and Somerset we are advising people to stay indoors.
"If you do have to drive, we suggest you slow down and brake, steer and change gear as smoothly as possible to avoid skidding."
B&NES said it had a good supply of salt for the next few days.
It said it would try to keep car parks open and urged people to use its network of 400 grit bins to treat their own roads - but to do so “sparingly”.
B&NES has alerted its army of volunteer snow wardens, and also has a number of farmers on stand-by to help with snow-ploughing.
No flights are taking off or landing at Bristol International Airport today.
Outpatient clinics run by Sirona Care & Health at St Martin’s Hospital, Bath, Paulton Memorial Hospital and Keynsham Health Centre are cancelled today.
For information on the latest situation, go to www.bathnes.gov.uk or www.twitter.com/bathnes.
Some trains were being delayed this morning and this afternoon.
Full bus service details are at http://www.firstgroup.com/ukbus/bristol_bath/travel_news/service_updates/?item=34701&conf=1
Both the city's universities were closed today, and outpatient clinics were cancelled at St Martin's and Paulton hospitals, and Keynsham Health Centre. Sirona's day services at Radstock and Carrswood were also cancelled.
The weather forced the closure of several shops and other businesses in the city centre.