Forecasters have issued a snow and ice warning for Sheffield and South Yorkshire from this evening.
The Met Office has issued a yellow warning for between 6pm this evening and 10am tomorrow morning.
In Yorkshire and the Humber strong gales are expected later today, with snow expected to fall over high ground overnight.
Temperatures in the region are expected to drop to -2C this evening, resulting in frost developing in some places.
Drivers using cross-Pennine routes on Monday morning have been warned to expect ice on the roads.
A spokesman for the Met Office said: “A cold westerly flow, originally sourced from Canada, will bring a mix of sleet, snow and hail showers later on Sunday and overnight.
“Once we lose the effects of daytime sunshine, snow will start to accumulate more widely, and along with ice may present some problems, in particular for road travel on Monday morning.
“This seems most likely for parts of Scotland, Northern Ireland and cross-Pennine routes.”
He added: “Northern areas of England and Wales will see snow chiefly over higher ground, with more than 5cm in places but with slight accumulations possible at low levels too. Ice will be an additional hazard across much of northern Britain.
“The public are advised to be aware of tricky travel conditions generally, and possible disruption to transport.”
The weather is expected to remain cold and windy throughout the week, with a severe wind chill over high ground tomorrow.