The 12/19/05 USA Today has an article entitled The Big Chill about what could happen if there is a winter fuel crisis.  Here are some telling quotes about the North East US, where I live (emphasis are mine):

While the Big Chill will hit low-income households the hardest, no one
may be immune if the weather turns foul. New England and perhaps all of
the Northeast, including New York City, are a special worry. Gas
companies grant big price breaks to customers year-round if they agree
to have their service cut when supplies are short. Chances are great
these discount customers will be shut down this winter, and they
include manufacturers, some schools and hospitals, and, ominously,
about 77 percent of New England’s gas-fired electric power generation,
which requires large quantities of fuel .

The curtailment of "interruptible" customers will trigger a double
squeeze on consumers throughout the Northeast. First, costs for home
heating oil will skyrocket, as scores of power plants and other
interruptible gas customers switch fuels and make a grab for all the
oil on the market. Even though heating oil is a major fuel source in
the Northeast, there are no oil pipelines from refineries into New
England, which relies on deliveries by tanker or barge. And in recent
years, the oil industry–following the U.S. industrial trend–has been
keeping inventories low to promote efficiency. Tim Irving, executive
director of Heat, U.S.A., a company that buys heating oil in bulk for
northeastern homes, recalls that in the most recent severe cold snap,
January 2004, the industry simply could not ship in sufficient
supplies. "The just-in-time inventory system, when put together with
the utility policy of having interruptible gas customers, creates a
very volatile situation where literally in a week, New York harbor went
dry [of heating oil shipments] because utility customers went on line,"
Irving says. "Your middle American ends up paying more to support this
situation."

Electricity could also be effected:

The second threat is a severe electricity shortage in the
Northeast–with possible brownouts or blackouts. Deregulated
natural-gas-fired power generators, under no legal obligation to serve
customers as the old monopoly electric companies were, can simply stop
generating power. Some plants will be interruptible customers with no
backup fuel source. But in other cases, power plants that have firm
natural gas contracts will stop generating electricity anyway and sell
their fuel at enormous profit. That is precisely what happened during
the three-day January 2004 cold snap, when more than 25 percent of New
England’s generating capacity went off line and the reserve margin was
near zero.  The market weathered that storm, but ISO New England, the
organization responsible for managing the electric grid, says that even
under normal weather conditions, electricity demand this winter most
likely will set a new record surpassing that of the perilous 2004 cold
snap. The grid operator has taken steps to head off a shortage,
spearheading a public-relations campaign to urge New Englanders to
conserve electricity, attempting to work out agreements with big
customers to curtail demand, and asking the Coast Guard to station
ice-breaking barges in locations that will assure fuel oil deliveries
can make it downriver to electric plants. But Connecticut Attorney
General Richard Blumenthal says as long as power generators are allowed
to shut down and sell natural gas during a weather crisis, there is a
risk of the kind of market chaos, as well as manipulation, that roiled
California in 2000 and 2001. "The result could be a calamity," he says.

Thanks to The Oil Drum for pointing this article out.