Temperatures dropped well below freezing overnight, and the cold snap is expected to last into Friday.
Snow has already fallen on high ground and there is a blanket of several inches on the Yorkshire coast.
Leeds has escaped so far - but wintry showers will be moving westwards into the city from mid-morning onwards.
The Met Office has predicted that some snow will settle, but it will only be deep on the hills.
The biting northerly wind will make it feel even colder than today's high of three degrees.
There will be more snow showers tonight, with several inches settling on higher ground.
Friday will remain cold and frosty, but the snowfalls will eventually tail off and the weekend is expected to be mild.