A majority of the deaths --18 -- occurred in Tennessee.
Three of those people died in a fire in Knox County, Tennessee emergency management officials said.
Family members said a man, woman and their adult son died in the fire, according to CNN affiliate WATE.
Firefighters said they had difficulty reaching them because the second level of the house collapsed onto the lower level, WATE reported.
Other people in Tennessee died from hypothermia and in auto accidents, WATE said, and a dialysis patient died after he was unable to get treatment because of weather.
More than 2,700 people are without power as more severe cold, freezing rain and snow are predicted for the next few days, Tennessee officials said.
Dangerously cold conditions continue to grip a large part of the Eastern United States, CNN meteorologists said, with more than 125 million Americans under a wind chill warning or advisory.
Wind chills will go as low as 40 below zero in some places.
Snow, sleet, and freezing rain will spread over the mid-South and into the mid-Atlantic over the next couple of days.
Ice storm warnings are in effect for Nashville, where heavy ice accumulation could again cause widespread power outages.
Winter storm warnings again cover much of Kentucky, which saw as much as 15 inches from the last storm.
More heavy snow is predicted for Louisville and Cincinnati.
The storm will spread up the East Coast this weekend.