According to the Met Office, there could be snow showers throughout the morning and again at around 8pm tonight.
A yellow weather warning has been issued for ice until around 10am.
The Met Office said: “Snow and hail showers could lead to icy surfaces, with possible travel disruption.
“What to expect – probably some icy patches on some untreated roads, pavements and cycle paths, leading to an increased chance of accidents or injuries
“Some higher elevation roads may be also affected by snowfall, resulting in longer journey times.”
The cold snap comes after Sheffield enjoyed temperatures of 20C last week.
The Met Office said it will feel cold with a wind chill today, but there could still be some good bright spells. Temperatures will reach a high of 6C.
Tonight, it is forecast that there will be occasional showers continuing through the night.
The showers will remain wintry although any snow accumulations will be mainly limited to high ground.
It will be cold with icy patches and frost developing in places, as temperatures drop to 0C.
Tomorrow will be bright but chilly and there will be occasional showers, which could include hail and sleet.
It will be cloudy and there will be occasional showers on Saturday, still wintry in places.
Sunday is set to be drier brighter.
Monday is looking breezier with the risk of rain.