More than 2,000 flights have been canceled amid the severe weather.
Deaths in Texas included a woman and a girl died from suspected carbon monoxide poisoning in Houston, at a home without electricity from a vehicle running in an attached garage, police said.
Texas law enforcement reported that two men were found dead along Houston-area roadways.
In west Tennessee, a 10-year-old boy died after falling into an ice-covered pond on Sunday during a winter storm, fire officials said. In some parts of the state, temperatures have plummeted to minus 18 degrees Celsius (1 Fahrenheit). By contrast, thermometers in Anchorage, Alaska read 20F.
"It's lovely to see the white but very risky at the same time because people here don't know how to drive in it", Houston resident Michael, who only gave his first name, told AFP.
Looking for large groups of people in places where they wouldn't have to drive and with appropriate medical personnel on hand, county officials distributed the doses at three hospitals, Rice University and the county jail.
At least 11 people died over the weekend in weather related auto crashes, including nine in Texas, one in Kentucky and another person in Oklahoma.
Across the southern border, Mexican officials said six people died after temperatures plunged and frozen pipelines bringing natural gas from the United States caused rolling power outages.
Three people died and at least 10 were injured when the tornado tore through a golf course community and another rural area just before midnight on Monday, destroying dozens of homes. Two agricultural workers also died in neighboring Tamaulipas from hypothermia.
The National Weather Service was "very surprised how rapidly this storm intensified ... and at the time of night when most people are at home and in bed, it creates a very unsafe situation", Emergency Services Director Ed Conrow said.
Northern Louisiana is in the bullseye for the highest amounts of freezing rain from the incoming system, forecasters said in a Tuesday briefing, and more than a foot (30 centimeters) of snow was possible in Arkansas, according to the federal Weather Prediction Center.
NY governor Andrew Cuomo on Monday ordered emergency services to prepare for sleet, ice and freezing rain.
Winter weather advisories are in effect for multiple states from coast to coast as a major storm batters the country. About four inches of snow fell at the Dallas airport. The weather had caused nearly 60 flight cancelations at local airports by Tuesday morning, the local ABC affiliate reported.