The cold winter and the natural gas shortage mean that the United States is now importing half the oil it burns every day.

Figures compiled by the American Petroleum Institute, a major industry organization, show that oil imports averaged more than 8.7 million barrels a day for the month of January, an increase of more than 30 per cent over January's imports a year ago and the highest monthly import average in the nation's history. More than half the oil imported into the United States in January came from Middle East countries like Saudi Arabia, Iran and Kuwait.

Energy experts in the Carter administration said they believe the high level of oil imports will continue at least through the rest of the winter, partly because of the cold weather, partly because of the shortage of natural gas and partly because U.S. domestic oil production continues to decline and cannot meet the rising demand.

The Carter administration now estimates that the oil import bill for the nation this year will be $40 billion, which would be an increase of $6 billion over the $34 billion paid out in 1976. At the same time, Federal Energy Administrator John F. O'Leary acknowledges there are so many uncertainties that the import bill could be higher than $40 billion.

"A lot depends on how many consumers in California and the Pacific Northwest have to switch to oil because of the drought and the shortage of water power," O'Leary said. "A lot also depends on when natural gas users who had already made the switch to oil can move back to nautral gas."

The same cold weather that caused oil imports to soar has also resulted in skyrocketing demand for electricity, much of it generated by oil-burning electric plants.

The natural gas shortage stimulated oil and electricity demand, as factories using gas switched to oil and as homeowners burning gas for heat turned down their thermostats and switched to electric heat. Portable electric heaters sold out in department stores in no fewer than six Eastern and Midwestern states.

New York's Consolidated Edison paid $75 million for imported oil in January. The biggest part of the bill went for heavy oil to burn in Con Ed's electric plants, but a rising portion was for kerosene and heating oil to run the turbines Con Ed normally uses only to meet peak demands for electricity in the hot summer months.

Con Ed figures it will pay at least $700 million this year for imported oil, which would be $200 million more than it paid last year. The big New York electric company will almost surely ask the state's Public Service Commission for permission to charge its customers higher rates.

Outside of New York, the six New England states in January paid an estimated $175 million for the heavy oil they imported to make electricity. That was an increase of more than 20 per cent over what they paid in January a year ago. New England also paid $500 million for kerosene and heating oil, much of it for imports.

Oil imports have been rising steadily ever since the Arab oil embargo ended in April, 1974, when the United States imported about 20 per cent of its oil. Imports rose to 33 per cent of the oil burned in the United States through most of last year, then rose sharply in December of last year when they totaled about 40 per cent of the oil used in the United States.

The daily import average of almost 8.8 million barrels a day for January puts the percentage of imports at about 50 per cent. Domestically, the United States produces about 8.8 million barrels of oil every day.

The chief exporters to the United States are Saudi Arabia, Iran, Kuwait, Venezulea and Nigeria. Venezuela stepped up its oil production last month to 2.4 million barrels a day from a pre-imposed ceiling of 2.2 million barrels to satisfy U.S. demand for heavy oil and heating oil.