Some lanes of the M62 have been closed due to the snow, while conditions are 'hazardous', National Highways has said.
The A628 Woodhead Pass is also experiencing tricky conditions, while A57 Snake Pass has been closed due to the weather.
The agency, which looks after major roads across the country, said: "#M62 remains hazardous in places due to snow between J21 and J23. Our winter maintenance crews continue to operate in the area. We are expecting more snow in the new couple of hours so please travel with care if your planning to use this section of motorway this morning.
"The conditions on the #M62 have improved and we now have at least 2 lanes clear of snow between J21 and J23 in both directions. As traffic increases the snow on will clear further. There are no delays in the area."
The Met Office's forecast for the next couple of days says: "Rain, sleet and hill snow moving northwards, easing later Sunday.
"Cold and cloudy as a band of rain, sleet and hill snow makes very gradual progress northeast, becoming lighter and more showery with time. Strong winds easing later. Maximum temperature 5 °C."
The snow should have gone by tomorrow, with the wet weather continuing later in the week.