EDF Energy said its staff are working in "difficult circumstances"
Hundreds of homes in the east of England, some of them in Suffolk, have been without power through the night.
Engineers from EDF Energy have been working to restore power but have been hampered by poor travel conditions due to high winds and snow.
EDF Energy said on Friday that the areas which might not be restored overnight include parts of Ipswich, Bury St Edmunds, Brandon and Wenhaston.
The British Red Cross is visiting the most vulnerable customers, it added.
In a statement, EDF Energy added that thousands of power supplies have already been restored.
"We have additional staff working to resolve these faults, but as travel conditions are so poor it is extremely difficult for our engineers to patrol our overhead lines and reach faults in many areas, even in four-wheel-drive vehicles," it added.
"Snow is still falling in some parts and further poor weather has been forecast.
"As a result, repairs will take longer than normal to complete.
"Our partners in the British Red Cross have been out to support some of our most vulnerable customers, and we are also proactively contacting those we know are in particular difficulty," it added.
"We appreciate how difficult it can be to lose power, especially in cold weather, and would like to apologise for the inconvenience this is causing."