Around 1,500 homes in Netherton are without power, Northern Power Grid has reported.
Engineers are currently trying to fix the problem, which also closed Netherton Junior and Infant School earlier today.
Firefighters have dealt with 186 emergency calls across West Yorkshire due to the storms so far today.
Of those calls, 80 involved dangerous structures including chimney stacks, loose roof cladding and signs.
Problems were also reported with fallen trees and trampolines which had been lifted by the wind.
Ian Bitcon, Area Manager for Fire Safety, said: “We have had an extremely busy day today. However, crews have dealt professionally with these incidents and had the necessary resources to do so.
“Fortunately, there has been no serious injury as a result of today’s weather.”
At Wakefield, Ossett and Normanton Stations firefighters said they had been busy but there were no serious incidents or casualties.
The Met Office has issued a yellow warning for ice until midday tomorrow.
Mr Bitcon added: “Given that we may well have icy weather on the way we urge the public to take extra care at home and on the road as the winter snap sets in.”
To contact Northern Power Grid call 0800 375675.