The A57 Snake Pass is closed from the A6013 for the Ladybower Reservoir to the Royal Oak Inn on Hurst Road.
The A6024 Holme Moss, between Rake Head Road and the A628 at Woodhead Pass, is also shut due to snow.
Winnats Pass is closed near Castleton.
A new yellow weather warning for snow was issued for parts of the Peak District, at around 10.15am, which covers northern parts of the county from 11am until 3pm.
A Derbyshire Counry Council spokesperson said: “Our gritters were out overnight gritting all primary and secondary routes and patrolling routes this morning, treating problem areas where necessary.
“Crews were back out on high routes in High Peak from 12.30pm and also in the Fairfield Common area of Buxton, trying to keep roads clear of snow.
“A band of sleet and snow currently hovering over the north of the county is expected to give way to rain later this afternoon.”
With further rain expected over the weekend there are currently flood alerts in place in Derbyshire.
Derbyshire Dales District Council has warned drivers and walkers ahead of anticipated flooding in the area, with the River Wye issued with a flood alert.