Storm Ciara has battered Yorkshire this weekend, with winds of up to 80mph and torrential rain causing travel chaos.
However, more inclement weather is expected for the next three days in the region.
The yellow warning for snow and ice will cover the region from 3pm on Monday until 12pm on Wednesday.
The Met Office said: "Showers will turn increasingly to snow later on Monday, becoming frequent and heavy at times and lasting through Tuesday.
"The snow showers will occur particularly over high ground giving locally 1-3cm above around 150 metres and 3-8cm above 300 metres.
"Snow will gradually build, perhaps leading to accumulation of 10-15cm on the highest routes.
"Any snow accumulations over low ground are likely to be temporary.
"Icy surfaces are likely to cause problems, especially overnight.
"Strong winds will be an additional hazard with gusts of 50-60 mph at times leading to drifting of snow over high ground."