Bus company First South Yorkshire hopes to run a normal service today, despite snow and ice on some roads.
Gritters are out across the city in a bid to keep traffic moving.
A First spokesman said: "After some snowfall overnight and low temperatures, we have seen a small layer of snow on local roads, and some icy conditions.
"The local gritting team have and are working hard to keep the highways moving, and at this time, we are endeavouring to run a full and normal service to all areas.
"At present, we are expecting to run a full service and no routes are reported affected. Nonetheless, if you are travelling today, please watch out for ice or snow on pavements - take a little extra time to be safe.
"We will keep you posted of any problems reported impacting on your local services."