Up to 8in (20cm) of snow have fallen in parts of Hampshire and the Isle of Wight.
The Met Office said more snow was due to fall later although coastal areas were expected to escape the worst of the weather.
Southampton Airport was shut but has now reopened. Passengers are being advised to check with the airline before setting off for the airport.
The A3 on the Hampshire/Surrey border was shut in both directions.
A police spokeman said there was a five-mile tailback northbound at Bramshott caused by lorries being unable to make it up the hill.
Christmas shoppers were warned not to drive unless necessary.
Hampshire Constabulary also advised partygoers to dress appropriately because of the freezing temperatures and icy winds.
Police said anyone needing to drive should stick to main roads which are on the priority gritting routes and be fully prepared with warm clothes, a hot drink, a shovel and a fully-charged mobile phone.
Hampshire Constabulary's 4x4 vehicles are on standby to help if needed.
South West Trains is running revised services but plans to return to normal on Sunday, weather permitting. The latest timetables are available on the company's website.