The warning is in place from 9am to 11.59pm on Wednesday, January 8.
Weather experts are warning that the cold conditions will cause icy stretches, with a chance that rural areas will be cut off and the possibility that properties will be affected by power cuts.
There is also a chance that the weather could cause travel disruption and delays.
The Met Office said: “Whilst not all areas may be affected, outbreaks of snow may push in from the southwest during Wednesday, potentially giving some significant accumulations in places. Two – five cm of snow could accumulate fairly widely, and as much as 10 cm over higher ground, especially over east or northeast-facing slopes. Rain or sleet is more likely near coasts. Note that there is still a possibility that the weather system, and associated rain or snow, may remain further south across the English Channel.
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“As precipitation clears eastwards and skies clear during Wednesday night, ice is likely to form on untreated surfaces.”
The Met Office is advising residents to take care while out and about in the snowy weather, to leave five minutes earlier if travelling, and to stick to main roads that are more likely to have been treated.
Hampshire County Council has announced on X that gritters have been out on priority routes due to road-side temperatures falling.
The post said: “Our gritters will be out later today on the priority routes as RSTs fall well below zero with a chance of sustained ice and hoar frost”.