About 33,000 homes and businesses are without power as of about 3:30 p.m., said Carol Peters, spokeswoman for Oncor Electric Delivery.
Peters described the outages as scattered and widespread throughout Dallas and Tarrant counties.
Red Cross officials, meanwhile, were waiting to hear from emergency management officials in those counties if shelters would be needed for people without power tonight. No word had been received by 4 p.m.
The overnight low temperature is expected to get down to 28 degrees, according to the National Weather Service.
Peters said snow was accumulating on tree limbs, which is causing them to sag onto the power lines. She said other outages were caused by vehicles sliding into utility poles. "We have crews out now investigating," Peters said earlier. "But in most cases we won't know how to fix the problem until they have a chance to investigate."
She said Oncor hopes to have power restored throughout Dallas-Fort Worth within 24 hours.
Peters asked residents without power to call Oncor at 1-888-313-4747. It would be helpful if residents have their electric bills available so that Oncor can pinpoint the outages, she said.
Red Cross volunteers have been placed on standby if they are needed to open shelters, said Anita Foster, Red Cross spokeswomen in Dallas.
"We have mobile vehicles -- basically, 'shelters in a box' -- with cots, blankets, etc.," Foster said. "We have them positioned in our response communities -- in Denton, McKinney, Corsicana and, of course, in Dallas."
Alyson Barber, spokeswoman for the Red Cross Chisholm Trail chapter in Fort Worth, said a lot of people tend to "hunker down" in cold weather. Foster added that road conditions may be too treacherous for people to try to reach shelters.
Therefore, Foster urged people to make preparations in case they are stuck at home with no heat.
For example: keep you gas tanks full; have extra firewood on hand for your fireplace; use flashlights, not candles for emergency lighting; stoke up on extra batteries, first aid supplies and non-perishable foods that can be opened and eaten without cooking.
Also, avoid driving when conditions are treacherous, but if you have to go out, make sure you go with extra blankets, warm mittens and kitty litter for wheel traction, in case you get stuck.
You can prevent hypothermia or frostbite by wearing warm, loose fitting clothes in several layers. Also, never use a generator indoors.