Leeds City Council said gritters had been treating roads overnight and road crews were mobilised to clear drifting on high routes.
Dozens of bus services have been suspended or diverted from some routes - FULL LIST HERE.
The Met Office has a yellow weather warning in place for Yorkshire and Humber.
A Met Office spokesperson said: "Snow showers are likely to continue throughout Sunday, with an increased chance that longer spells of snow will affect some areas."
Drivers have been warned not to travel unless necessary due to snow and ice.
South Yorkshire Police said roads in South Yorkshire were 'horrendous'.
The M1 is currently running as a single lane, the Woodhead Pass and Snake Pass are closed and many roads around Yorkshire are treacherous.