After Trans-Siberian Express—the name of a railway running from Moscow to Vladivostok on the Sea of Japan—, the informal American-English phrase Siberian Express denotes a surge of extremely cold air which causes rapid falls in temperature and severe wintry weather in central and eastern areas of the United States and Canada.
—Cf. also ‘the Beast from the East’ | ‘the Pest from the West’.

Typically, a Siberian Express is generated by an area of high pressure formed over Siberia between November and March, and is carried over the North Pole and south across Canada by the jet stream before being driven eastwards by winds from the North Pacific.

However, the earliest occurrence of Siberian Express that I have found does not refer to North America, but to Japan; it is from an article about a tidal power plant at Yura, in Japan, by Henry Scott Stokes, of The New York Times (New York City, N.Y.), published in the Corvallis Gazette-Times (Corvallis, Oregon) of Thursday 6^th March 1980:

The Japanese, short of cheap energy resources of their own, lacking oil altogether and wholly dependent on the price whims of their Middle Eastern suppliers, are experimenting with all possible alternative sources. Among them are the seas that strike this icy shore, lashed in winter by the so-called Siberian Express, the northwest wind that comes across the Sea of Japan at 70 miles an hour at times, pushing up 30-foot waves.

The second-earliest occurrence of the phrase Siberian Express that I have found is from an article by David L. Langford, of the Associated Press, published in many newspapers in January 1982—for example in the Albany Democrat-Herald (Albany, Oregon) on Saturday the 16^th:

A surge of polar cold nicknamed the “Siberian Express” blew into the frozen Midwest with paralyzing blizzards Saturday, and the mercury sank to painful lows deep into the Sunbelt.
[…]
“It is one of the most severe outbreaks of cold weather mid-America has seen since the 1800s,” said meteorologist Nolan Duke of the National Weather Service in Kansas City.
[…]
Duke said the cold is coming from the polar regions of Siberia, prompting one meterologist [sic] to dub it the “Siberian Express.” Unlike normal winter weather patterns in which the systems move across the warmer waters of the Pacific, the present air is taking a northerly track across the polar regions of Canada.

The following is from The Courier-Journal (Louisville, Kentucky) of Wednesday 3^rd February 1982:

How OPEC revived a sagging U. S. industry

The buggy whip business and the long-handled underwear trade went sour about the same time. The former probably was mourned much more than the latter, except perhaps by horses. The real blessing of central heat, the old timers say, was mostly in the opportunity to throw away the scratchy red flannels of yesteryear.
But it’s the long johns, not the buggy whips, that have come back, as an Associated Press story observes. Not the scratchy underwear of old, or the scarcely more comfortable woolies that kept GIs from freezing. Now there are double-layered cotton-wool combinations and all-cotton thermal weaves that soothe as well as warm. For the fashion-minded, there are new patterns and colors—though old-fashioned red still has its adherents.
The Arabs, with their high oil prices, did it. One major maker of long handles has trebled its business over the past five years as heating bills went up and home thermostats went down. Like insulation, long underwear is cheaper than oil, or even gas.
Things are even better, or worse, during the current tough winter. One long underwear producer still has its normally large pre-Christmas staff of telephone answerers on the job, mostly answering emergency pleas from such places as Florida, California and Texas. “Those people are just freezing,” a supervisor says.
The ill wind that will bring back buggy whips hasn’t yet blown. But it’s comforting that the blasts of this winter’s Siberian Express have warmed at least one spot in a chilly economy.

This cartoon was published in The Mobile Register (Mobile, Alabama) of Friday 5^th February 1982:

“Be careful… If they came in on the Siberian Express cold wave, they could be Russian spies!”