The tornadoes touched down in the tiny coastal town of Keaton Beach in Taylor County and Capitola in Leon County, a neighborhood on the outskirts of Tallahassee, state emergency officials said.
Leon County Sheriff's Deputies say about a half-dozen houses were damaged, reports WTCV-TV in Tallahassee.
Power lines were brought down, but there were no reports of serious injuries or deaths.
Up to a foot of snow was possible in several areas in the nation's midsection.
"It could get real nasty," said Dusty Harbage, a National Weather Service meteorologist in Jackson in eastern Kentucky, a region expected to be on the tail end of the wintry blast.
The snow in Texas came on top of a storm system Thursday that left as much as 9 inches of snow on northern parts of the state and brought a tornado to the south part of the state.
A twister packing 95 to 105 mph winds in Corpus Christi on Thursday afternoon, but trees were snapped and several homes were damaged, said Roger Gass, a National Weather Service meteorologist in Corpus Christi. About 20 homes in northern Lake City were damaged, with a handful of homes destroyed in Capitola, a neighborhood on the outskirts of Tallahassee.
The weather service said the Louisville, Ky., area could expect 8 to 12 inches of snow, starting Friday morning. The heaviest snow is expected Friday night and early Saturday, when 4 to 5 inches could fall within six or seven hours, said Joe Ammerman, a weather service meteorologist in Louisville.
In the Frankfort and Lexington areas, 6 to 10 inches could fall, with 4 to 6 inches across south-central Kentucky. In eastern Kentucky, forecasters say rain during the day Friday will change over after midnight to freezing rain, sleet and then snow.
"It's not uncommon to get big snows in March," he said. "The one good thing about that is it tends to warm up fairly fast and the snow doesn't stay around very long."
In Arkansas, Weather Service forecaster John Lewis said conditions in Little Rock could be particularly hazardous by Friday evening.
The winter storm Thursday left slick roads in North Texas that sent some school buses into ditches and hundreds of cars off the roads.
South of Gainesville, several buses from the Callisburg school district slid into ditches as students from all grades were being taken home early Thursday because of the weather, Cooke County Emergency Management Coordinator Ray Fletcher said.
The children walked out through the main doors except in one case, where the bus slid onto its side and they had to escape through a back door, he said. No injuries were reported.