The National Weather Service warned "dangerously cold air" across the US combined with strong winds could result in frostbite if residents don't wear hats, scarves and gloves. Photo: EPA

High winds mean wind-chill temperatures are forecast to drop as low as -50F (-45C) in Minnesota.

The freeze has led to the closure or late running of schools from north to south, from the Dakotas to Alabama.

Winter weather warnings have been issued for 17 US states and for Ontario and southern Quebec.

In other developments:

• heavy snow and blizzards forecast in North and South Dakota
• temperatures will plunge to -44F (-42C) in Fargo, North Dakota
• schools are closed in Chicago, in -28F (-33C) temperatures
• a storm dumped about a foot (30cm) of snow in northern New York
• another foot of "lake-effect" snow is expected in parts of New York state over the next two days

In the north-east, temperatures were expected to drop further on Wednesday following an arctic blast of air that could produce wind gusts of up to 40mph (64km/h).

The National Weather Service warned "dangerously cold air" across the US combined with strong winds could result in frostbite if residents don't wear hats, scarves and gloves.

New York Mayor Bill de Blasio urged residents to check in on neighbours and relatives who may be at risk.

School districts in Indiana, Wisconsin and Minnesota were also closed because of the cold.

Meanwhile in California, a winter heat wave has temperatures topping 80F (27C).