The driver of the Peugeot 207 was travelling down Kirkgate at around 11am when he skidded on the ice and lost control of his car.
In order to avoid carrying on straight through the crossing gates, the driver steered right before crashing into the north-bound platform at the station.
The car, which had become wedged between two walls, was recovered by police an hour later.
Platform 1 was closed whilst work was carried out to stabilse the wall before Network Rail engineers installed a temporary barrier.
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The crash did not affect the running of the trains and the temporary barrier will remain in place until the wall can be permanently repaired.
The driver, a man in his 20s, was not injured in the crash.