The yellow alert is in force for much of Sunday starting from 3am and lasting until 6pm.
It follows a previous weather warning for snow and ice which came into force at 4pm on Friday and remains in place until 10.30am today.
The alert for Sunday covers parts of Portsmouth including Hilsea and Cosham, but has not been issued for the whole city.
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The snow warning is also in force for Fareham, Havant and Waterlooville.
On its website the Met Office says: ‘A band of rain will turn readily to snow as it spreads eastwards leading to possible transport disruption.
‘Mainly 1-3 cm of snow accumulation for most parts, but possibly 5-10 cm over 100 m with a small possibility of 10-15 cm over high ground for example on Dartmoor, the Brecon Beacons and Snowdonia.
‘These snow amounts will cause some disruption to transport, especially on routes that cross even modest high ground.
‘Some roads and railways likely to be affected with longer journey times by road, bus and train services with the potential for some roads to become blocked on higher level routes.
‘Probably some icy patches on some untreated roads, pavements and cycle paths.’
The Met Office is currently forecast spell of cloudy weather and sunny intervals for Portsmouth today, with highs of 5C and lows of -1C, followed by heavy rain changing to cloudy by the afternoon on Sunday.
Sleet is being forecast for Swanmore and Winchester tomorrow while Petersfield and East Meon could see light snow in the morning.