Deal and Atlanta Mayor Kasim Reed were the targets of criticism Wednesday by those who found themselves sitting on gridlocked highways or had children stuck in school buses or at schools overnight.
Deal apologized for the situation but said his administration had responded in "reasonable" fashion to the situation, the Atlanta Journal-Constitution reported.
"We can never promise that we will always be correct when it comes to deciding what Mother Nature will do," he said. "She truly does have a mind of her own."
Reed acknowledged mistakes were made, but said his main priority is getting people back home, the newspaper said.
"What I'm thinking of every moment is how to get people out of their cars," Reed said. "I'm not going to get into the blame game, but the crisis that we are going through is across the region. If you look at anybody's street in any community across the entire region, there's no one doing a better job than we are in the city of Atlanta."
Deal said state government would be closed a second day Thursday, and both he and the mayor urged people not to drive so emergency crews could deal with stranded motorists.
"I have told state employees to not report to their offices tomorrow in an effort to limit traffic," he said. "I encourage others to do the same. With rising temperatures, we hope to return to normalcy [Thursday]."
CNN reported it wasn't much different in neighboring Alabama, where Gov. Robert Bentley said some interstates were "still treacherous."
"The traffic is still proceeding very slowly, but we are making progress," he said. "We still have a number of students around the state that could potentially have to remain in school tonight but they will be taken care of. They will be protected. They will be fed. They will stay warm."
Freezing rain made driving perilous across Alabama where officials said at least five people died in weather-related traffic accidents, CNN said.
Law enforcement officials in Alabama and Georgia reported motorists were stranded as long as 12 hours because ice and snow turned roadways into parking lots, CNN said.
Bentley has declared a state of emergency and deployed 350 National Guard troops. States of emergency also were declared in Louisiana, North Carolina and South Carolina.
Rebekah Cole left work in Atlanta Tuesday afternoon and was still trying to go home at 1 a.m. EST Wednesday.
As she prepared to spend the night in her car, she told CNN she hoped it wouldn't run out of fuel.
"If I get gasoline, I will turn the heater on, keep the windows cracked a little bit," she said.
As much as 10 inches of snow fell in parts of Virginia Tuesday and Tuesday night, including as much as 8 inches in Virginia Beach, AccuWeather.com said.
The wintry weather moved eastward across Georgia, South Carolina, North Carolina and the mid-Atlantic coast Tuesday night, creating hazardous travel conditions along the Interstate-10 and I-95 corridors.
Travelers stranded by the storm sought out strangers' homes, schools, even the big-box hardware chain Home Depot, which opened 26 stores so travelers could escape the elements in Alabama and Georgia, CNN said.
School systems across the south canceled classes Tuesday and Wednesday.
The severe weather forced 4,500 students to spend the night in school buildings in Hoover, Ala., and 800 students were stuck in schools in Birmingham, officials said.
"Staff is staying with them, feeding them," Birmingham City Schools Superintendent Craig Witherspoon said. "High schools are showing movies."
Hartsfield-Jackson Atlanta International Airport canceled nearly 500 flights early Wednesday. Thousands of flights were canceled at airports across the South Tuesday, including the Atlanta airport and George Bush Intercontinental Airport in Houston.
Alexandria, La., Tuesday broke a 110-year-old record with 1.2 inches of snow for the date. The previous record was 1 inch, set in 1904, the National Weather Service at Lake Charles said.
Tens of thousands of power customers were without power in several states from Florida through Virginia as of Tuesday evening, utility officials said.
Celebrity Families of 2014 [PHOTOS]