The freezing conditions are expected to continue over the coming days as a strong jet stream continues to pull cold air over the UK.
The Met Office has issued another yellow weather warning for ice, which is expected to form on some surfaces from late afternoon and last overnight into Wednesday morning.
There is a chance of rain showers, which will quickly freeze, and a few centimetres of fresh snow on higher ground.
A Met Office spokesman said: "There will probably be icy stretches on untreated roads, pavements and cycle paths with some injuries possible from slips and falls. There is also a very small chance of travel disruption across parts of Scotland and northern England."
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Full forecast for Yorkshire:
Tonight: There is a risk of icy patches this evening as outbreaks of rain, sleet or hill snow spread east and fall onto frozen ground. Breezy and clearer conditions will follow. Minimum temperature 0C.
Wednesday: Showers will quickly arrive through the morning, becoming frequent, sometimes heavy and also wintry, although mainly over high ground. Showers clear east through the afternoon, sunny spells follow. Breezy. Maximum temperature 6C.
Outlook for Thursday to Saturday: Generally rather cold. There will be overnight frosts, and so an ice risk as sometimes wintry scattered showers will continue Thursday and Friday, before dying away through Saturday.