President Joe Biden has approved a state of emergency in Texas where a surge in demand for electricity has led to widespread power cuts.
The National Weather Service (NWS) said more than 150 million Americans were now under winter storm warnings.
Kentucky, Mississippi, Alabama, Oregon and Oklahoma are among states affected.
The freezing storm even reached northern parts of Mexico where more than four million homes and businesses lost power early on Monday.
Icy roads have led to a spate of traffic accidents. In Houston, Texas, nearly 120 road crashes were reported on Sunday alone. A pile-up on a major highway near Oklahoma City during a snowstorm on Sunday left several lorries on fire.
Travellers in several states have also been warned that flights could be delayed or cancelled. In Houston, Texas, the George Bush Intercontinental Airport and the city's Hobby Airport were both closed until at least Tuesday.
The NWS said unusual meteorological conditions had allowed an "Arctic outbreak" that originated just above the US-Canada border to spill out into and across the US.
"Over 150 million Americans are currently under winter storm warnings, ice storm warnings, winter storm watches, or winter weather advisories as impactful winter weather continues from coast to coast," the NWS said in a statement.
"Hundreds of daily low maximum and minimum temperatures have been/will be broken during this prolonged 'polar plunge,' with some February and even all-time low temperature records in jeopardy."
Up to 12in (30cm) of snow are expected across parts of the southern Plains - the large area that spans parts of Texas, Oklahoma and Kansas - according to NWS meteorologist Marc Chenard.