The red Ford lost control and mounted the curb, before ploughing into the front window of the property on the residential street.
The scene, on Argyle Road in Sheffield, was captured by social media users as they made their way to work in the treacherous conditions.
Elsewhere in Yorkshire, Leeds Bradford Airport was forced to close due to the snowfall, but has now reopened, and has told passengers to continue to arrive as normal.
A spokesman for the airport said it shut after around 5cm of snow came down during the night.
The spokesman said snow ploughs and gritters had been working along the runways and despite the delays they were working towards ensuring all flights left as planned.
Holidaymakers had so far been understanding about the problems caused by the difficult weather, the spokesman added.
Dozens of schools across the region opened late or planned to close early, with South Yorkshire, Derbyshire and parts of Bradford and Kirkless worst affected.
In Sheffield, eight schols were closed - most of them special schools - with 16 opening late and one closing early.
In Kirklees, eight schools were closed, including schools in Birkby, Helme, Hepworth, Holme, Paddock, Scholes and Skelmanthorpe.
Eleven closed in Calderdale, including schools in Barkisland, Cragg Vale, Lee Mount, Luddenden, Ripponden, Sowerby Bridge, Todmorden and Wainstalls.
West Yorkshire Police warned people to take extra care on the roads, posting on Twitter: “Please take extra care when driving today in these cold & icy conditions. We want you to get to your destination safely.”
The Met Office is forecasting further snow for the region and many other parts of the UK during the morning.
But conditions will improve tonight and temperatures are forecast to rise towards the weekend, with some sunshine for Saturday.