Cumberland Council is advising people to check its live weather cameras, which cover roads right across the county, and to check conditions before travelling.
National Highways announced earlier the A66 would be closed from 07:00 in both directions between Augill Beck and Scotch Corner.
Several events have been cancelled or postponed, including a fireworks display in Whitehaven and the Taste Cumbria festival in Cockermouth.
The Carlisle United game against Newport County has also been called off.
The Blues were due to travel to Wales for the clash, but the country is covered by a rare red weather warning, external.
Storm Darragh strikes the UK on the same date as Storm Desmond hit in 2015, which was described as the largest to affect Cumbria in 600 years.