The Met Office said last night that rain, sleet and snow should gradually be confined to the south east of the Yorkshire and Humber region.
Drier and brighter conditions with scattered wintry showers were due to develop further north and west.
It is set to be cold and bright across Yorkshire tomorrow and Monday, with scattered wintry showers and overnight frosts.
A reported 80 schools were closed across West Yorkshire yesterday as residents across the county woke up to a blanket of snow.
Forecasters warned that the sleet and snow which caused traffic chaos across Yorkshire and hit flights to and from Leeds Bradford Airport was set to continue last night.
Both carriageways of the M62 near Huddersfield were closed for a short time yesterday afternoon after a crash involving a car and a lorry.
Police and fire crews were called to the incident on the westbound M62 near junction 23 for Huddersfield just before 1.30pm.
The eastbound and westbound carriageways of the M62 were closed for a short time at the accident scene to allow the Yorkshire Air Ambulance to land on the motorway.
One male casualty, who suffered non life-threatening injuries, was flown to Leeds General Infirmary for treatment.
Leeds Bradford Airport was closed for a time yesterday morning. It later reopened, though many flights were delayed. The greatest snowfall, up to 3.9in, hit the Peak District and the Pennines yesterday as daytime temperatures in northern England struggled to reach 4C in Leeds and Manchester, and 3C in Bradford. At Newby Head in Hawes, North Yorkshire, a council gritter had been working to clear five inches of snow on the road.