Two to three inches of snow fell on the hillier suburbs and eastern parts of Brighton and Hove overnight.
Heavier falls north of the Downs affected journeys to and from Brighton and Hove by road and rail.
Southern reported disruption to train services with some journey times about 30 minutes longer. Some trains were cancelled and others were delayed.
Sussex Police urged drivers to take care and adapt to the slippery conditions on many roads.
Vehicles were involved in minor accidents on the A27 Brighton Bypass at Hangleton as well as in Falmer and on the A23 north of Brighton.
Brighton and Hove Buses said that it was diverting some services and shortening the routes of others.
A power failure affected about 50 homes in Hove.
And Brighton and Hove City Council opened its emergency shelter for the homeless while sending out its new fleet of gritters.
The council said: “We’ve opened an emergency shelter for rough sleepers during the cold weather. Please check on vulnerable friends and neighbours.
“If the Met Office weather forecast predicts at least three consecutive nights of below zero temperatures an emergency shelter is opened.
“The city’s rough sleepers outreach team works flat out to make contact with as many homeless people as possible to let them know.
“The rough sleepers team is run by the CRI charity on behalf of the council. The shelter is run by staff from Brighton Housing Trust and CRI, with agencies across the city working together to ensure people are referred in.
“The city’s rough sleepers hotline is Freephone 0808 1680414 – or email Brighton.email@example.com.
“Residents can also use this number to report rough sleeping when they become aware of it. Reports enable us to reach as many people as possible.”
The council also urged people to check on vulnerable neighbours, saying: “Please check on any elderly and vulnerable neighbours as they may have needs around food, medicine or care.
“Elderly and vulnerable people should call the council’s adult social care helpline on 01273 295555 if they are having problems getting the services they require.
“We work with different providers around the city to ensure that all priority cases are covered during disruption.”
The council said that staff had been out gritting roads and pavements over the weekend and expected slightly warmer weather in the area in the coming days.
But rain overnight tonight (Sunday 5 February) and early tomorrow could freeze, making conditions treacherous first thing.
The council said: “This year Brighton and Hove City Council has a brand new fleet of gritting vehicles, a new motorised pavement gritter and has increased the number of grit bins in the city.
“However, we are not able to grit every road and pavement.
“During severe cold weather we prioritise clearing the roads and pavements which will help keep the city moving as much as possible.
“Government advice states it is legally safe for people to do this.
“We recommend you concentrate on steps and slopes and clear snow early in the day to let any sun melt the underlying ice.
“Avoid piling snow in the way of roads and footpaths.
“Table salt can be used to treat surfaces. One tablespoon will treat one square metre. Grit and salt should be used, not hot water which can refreeze.”
It added: “During the severe weather last winter owners of 4×4 vehicles came forward to help the council deliver essential services such as meals or medicine, home care staff and district nurses to residents who were out of reach with normal vehicles.
“We are always looking to have a list of people we can call on if needed.
“If you are able to volunteer or would like more information, please email Icanhelp@brighton-hove.gov.uk.
“Volunteers will only be used when the bad weather conditions are likely to run for several days and the demand for 4×4 vehicles exceeds the number of vehicles currently available to the council, police, fire and ambulance services.
“Despite thorough planning, we have to recognise there are limited resources and heavy snowfalls or a prolonged freeze do cause serious disruption.
“Residents clearing snow and checking on neighbours does make all the difference.
“We really appreciate the contribution of our residents and businesses in doing their bit to clear snow and ice and help neighbours.”