Interstate highways were in fair condition, but there were concerns about ice on the roads, said Pete Poore, spokesman for the Department of Transportation.
There has been virtually no melting: Temperatures ranged from 28 degrees in Rock Hill to 33 in Beaufort.
Nearly 1,300 workers were spreading salt, sand and salt brine on the roads. Using more than 700 pieces of equipment, workers had used nearly 20,000 tons of salt, 5,200 tons of sand, and 642,000 gallons of salt brine by Tuesday morning.
Poore urged motorists to stay off the road except in emergencies.
Steve Mesick said that wasn't an option for him. The 36-year-old Gaston resident had to go to work at a Columbia gas station.
"You just have to stay off the ice," said Mesick, laughing as he emerged from his car and skated across the ice in the parking lot. "Everyone needs gas, and someone needs to be here."
About 7,500 residents had no electric service Tuesday morning. Progress Energy reported the biggest problems from Cheraw to Lake City and Sumter, with more than 4,000 customers without service.
Duke Energy had about 2,400 customers without service, mostly in York County.
South Carolina Electric and Gas Co. reported about 400 customers without service Tuesday morning, mostly around Allendale and Barnwell counties. The Cayce-based utility said it had a peak of 4,000 customers without power overnight and credited its extensive tree-trimming program last year with helping to minimize outages from branches snapping under the weight of snow and ice.
The Dorn VA Medical Center closed its clinics Tuesday in Anderson, Greenville, Rock Hill and Spartanburg. The Columbia center planned to operate on a two-hour delay.
The South Carolina National Guard put 142 soldiers on active duty, mostly to help with traffic problems and to provide transportation for emergency workers.
At Fort Jackson outside Columbia, Army spokesman Pat Jones said the installation's offices were closed Tuesday and planning for a two-hour delay Wednesday.
The 8,500 soldiers currently in basic training were working with their drill sergeants in the barracks and study rooms because of the weather and hazardous road conditions.
"They won't be going out into the field," Jones said. "They have plenty to do inside."
Mitch Weiss in Greenville and Susanne Schafer and Jeffrey Collins in Columbia contributed to this report.
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