The yellow alert starts at 11am on Tuesday and ends at 11.59pm.
A Met Office spokesperson said: “A band of rain will turn to snow across northern England and Scotland through Tuesday.
“2-5cm is expected to accumulate quite widely across the area, but locally this could reach 10cm.
“Strong southeasterly winds will also lead to snow drifting in places, particularly over the highest routes, adding to poor visibilities.”
According to the Met Office, snow, heavy at times, could fall in parts of the Peak District throughout Monday. People are advised to check the weather forecast before they travel.