The Met Office earlier warned of 'wintry showers causing icy stretches' and said there could be slips and falls on icy surfaces, icy patches on roads and delays to public transport.
The roads around Meadowhall however appeared to be clear for vehicles despite the snowy conditions, and traffic seemed to be flowing well.
But in Gleadless, a reader said several vehicles were spotted getting stuck in snow at around 2pm and the road was deemed impassable.
National Highways said there were long delays on the M1 between J34 (Rotherham) and J37 (Barnsley) due to heavy snowfall in the area.
Stagecoach Supertram also issued advice to passengers, saying that they were unable to run trams between Sheffield station and Birley Lane due to abandoned cars on Park Grange Road.
Sheffield City Council's Street Ahead said their gritters have cleared several main routes in the city centre, including Bernard Road, Moore Street Roundabout, Gleadless Townend and Sheaf Square.
The Met Office said wintry showers are forecast to continue in eastern parts this evening, but gradually easing overnight.
However, the temperature could plunge to -3°C with a widespread frost forming overnight and patches of ice on untreated surfaces.
On Monday, it will be a mostly dry and bright but frosty start in Sheffield and cloud is likely to increase in the afternoon.
Forecasters also said there could be outbreaks of rain and brisk winds spreading in later with a maximum temperature of 4°C.