A taxi driver was hurt after sliding off the road and down an embankment
Freezing weather has caused travel disruption and led to the closure of about 187 West Yorkshire schools.
Black ice caused a number of accidents and in one incident, a truck crashed into a house near Leeds.
A number of roads were closed and buses in Bradford, Huddersfield and Keighley were suspended in the rush hour.
Police said routes in north-west Leeds, including roads in Stanningley, Otley and Calverley, had been closed due to cars skidding on ice.
Some flights have been affected at Leeds Bradford Airport but passengers are advised to check in as normal.
West Yorkshire Fire Service has reported a spate of incidents on icy roads, including two involving vehicles hitting buildings.
A man was taken to hospital after a taxi went down an embankment and ended up on the roof of a factory in Broadlands Road, Meltham, near Huddersfield.
Some people crawled across the icy roads. Pic by Rob Cartwright
A service spokeswoman said the incident happened at 0529 BST and three fire crews were called to the scene.
She said an earlier incident in Bruntcliffe Road, Morley, near Leeds, involved a lorry hitting a house.
One person from the truck was taken to hospital after the crash at 0141 BST and 20 firefighters were called to deal with the incident.
The spokeswoman said road conditions in West Yorkshire were "hazardous".
Yorkshire Ambulance Service said it had received a high number of weather-related 999 calls.
The service said non-emergency transport had been cancelled for patients due to attend routine appointments at hospital clinics across the region.
In Holmfirth earlier, almost all roads were described as impassable to cars and pedestrians due to slippery surfaces.
Additionally, Yorkshire Water said it was dealing with 80 burst pipes across the county.
Leeds City Council said primary routes in the city were being gritted.
A spokesman said bin collections were also being carried out but crews were assessing these on an individual basis depending on the conditions of the roads.
Residents were being advised to put rubbish out as normal on their usual collection days.