The Met Office has issued the alert from tomorrow afternoon until Friday night for Portsmouth and the surrounding area.
Yellow weather warnings have been put in place across parts of the United Kingdom for the next few days.
Traffic Scotland reported snowfall on parts of the M80 and M77 on Tuesday morning while Amey reported snow on the M8, M9 and A7. Widespread overnight frost is expected to develop with the maximum temperature 4 °C.
A Met Office forecaster said: "A band of rain, sleet and snow will move eastwards through the day and overnight bringing accumulations in some places".
Snow and Ice warnings for Thursday between 1.00pm and Friday 9.00pm for East Midlands, East of England, London & South East England, North West England, South West England, Wales, West Midlands and Yorkshire & Humber.
The warning reads: "Some roads and railways likely to be affected with longer journey times by road, bus and train services".
A warning for ice and snow, possibly heavy, remains in place for this evening and tomorrow morning, but has been brought forward to 5pm and the amount of snow has been reduced.
"It's not possible at this stage to be certain where exactly will see the worst impacts of any snow, but people need to be prepared for the possibility of disruption and make sure they check the forecast regularly".
Mr Burkill said: "It's what happens on Thursday that has the potential to be more disruptive". Thank you Julie Sadler for this picture taken near Skegness.
A deep freeze crippling Britain with "treacherous" winter weather including "very significant snowfall" and sub-zero temperatures has plunged Britain's transport networks into chaos. We have already got a warning out in force for it.
"It's looking like it will be a spell of persistent snow".