The Met Office issued the rare red weather warning on Thursday between 16:00 to 23:00, which caused major damage and disruption across the county.
Red warnings say “exposed places” are most at risk, bringing the risk of falling debris and a danger to life.
The storm saw gusts of up to 100mph (160km/h) in Cornwall and the Isles of Scilly.
Cornwall Council said the storm had been “one of the most severe” the county had experienced “in living memory”, with crews working around the clock to clear fallen trees and carry out emergency repairs.
The clean-up is continuing into the weekend.
A yellow warning for ice, external, including in parts of east Cornwall, issued from 12:00 GMT on Friday is due to end at midday.
More than 34,000 premises are still without electricity in the south-west of England, the National Grid said.
Staff were working “tirelessly” to fix issues, it added.