The severe weather warning is effective until Sunday (January 23) and the council has asked residents to 'please look out for vulnerable friends and family.'
Residents are also being advised to heat their homes to at least 18 degrees.
Due to the cold weather, the council's Severe Weather Emergency Protocol has been activated, which means rough sleepers will have access to a bed until Sunday, should they wish for one.
To access SWEP, clients will need to attend the Stonepillow hub at Glenlogie in Bognor Regis at 6pm on the night they wish to be offered a bed.
Arun District Council partner agencies and outreach teams have attempted to notify all rough sleepers of of the offer, and clients in Littlehampton who may struggle to get to Bognor Regis are asked to attend Turning Tides by 11am or to contact the Housing Options Team afterwards for help getting to Bognor Regis for the evening.
If you see a rough sleeper, please report them by clicking on this link: https://www.streetlink.org.uk/.
All referrals will be followed up by Arun District Council teams, who will be able to offer appropriate support.