Helicopters are being used to help restore power to hundreds of homes without electricity in North and East Yorkshire and northern Lincolnshire.
Engineers are using helicopters to assess damage to power lines
The aircraft are scouring the landscape to locate damaged power lines.
Blizzards left 7,000 homes without power on Friday and engineers worked into the night to restore supplies.
By Saturday afternoon, fewer than 1,000 remained without electricity and power company CE Electric said most would be reconnected by early evening.
Plea for patience
David Gill, head of customer services at power firm CE Electric, said: "Our engineers, overhead linesmen and field staff have been doing a fantastic job, often in the dark and in the face of difficult weather conditions.
"We're committed to getting everyone's lights back on in the least amount of time and we won't be downing tools until the job is done.
"Since first light today, engineers have been up in helicopters, surveying our extensive overhead powerline network in North Yorkshire to pinpoint and assess any outstanding areas of damage.
"This will allow us to promptly dispatch staff and materials to these often remote locations.
"Engineers are continuing to encounter access problems, such as fallen trees, but they are overcoming them.
"Our message to customers still without power is please bear with us, we will get your lights back on."
Water supply cut
The worst-hit areas of North Yorkshire are in Farndale, Kirkbymoorside and Rosedale on the North York Moors.
Meanwhile, 81 homes north of Pickering are without water after a power cut affected a pumping station at Newton Rawcliffe.
Engineers at Yorkshire Water said they hoped to get a generator installed as soon as possible.
In East Yorkshire, most of the properties without power are in villages north of Beverley.