Natural gas supplies continued to dry up rapidly today in the face of the harshest winter temperatures in decades, draining power from hundreds of factories, schools and some power generating plants in the eastern half of the nation.

As the deep freeze tightened its stranglehold on the Eastern Seaboard, municipalities from Kansas to Vermont grappled with the problem of how to lessen energy demands without dislocating the economy through factory shutdowns or panicking the citizenry with institutional or residential gas use cutbacks.

Scores of gas-heated school buildings in upstate New York were shut down because of the crisis; some major universities closed their doors in Ohio and Illinois, and factories scattered across the northern industrial states curtailed their production by either shutting down outright or laying off some shifts in an effort to conserve energy.

The nation's four major auto makers reopened a dozen plants they closed on Monday in Michigan and New York, but they closed two more in Ohio, idling 9,5000 workers. In Muncie, 56 plants were closed, and in Nashville, gas supplies were witheld from 76 industrial customers.

In all, upwards of 100,000 workers have been put off the payrolls, and a quarter-million students in eastern and midwestern states have been sent home because of the scarcity of fuel needed fo fire natural gas furnaces.

The dimensions of the problem were minimized in statements by federal and state energy officials, who said even a temporary slackening of the sub-freezing temperatures would alleviate the energy demand.

"We're praying for a nine cloud cover and some warm winds from the south. If they come, the demands everywhere will be less, and the problem may go away - for now," said an official of the New York State Public Service Commission. He noted that a rise in temperature in Buffalo from minus 14 degrees to 4 degrees above, plus a decline in wind velocity, already has improved the natural gas availability there, even if only slightly.

A spokesman for the Federal Energy Administration said the government projected that use of 1.84 trillion cubic feet of gas would be used in a normal year, 101 billion cubic feet more than the agency projected for last year.

"The problems of the last several days came as no big shock to us," the official said.

Energy officials said they don't have the data to pinpoint how much more gas is being used now. They pointed out that there is not so much a shortage of natural gas as a reduction of pressure in transmission lines caused by exceedingly heavy demands stemming from the cold.

Coupled with sporadic freezing of some transmission lines and freezing problems at some natural gas well heads, the pressure loss has created extraordinarily heavy "drawdowns" over the past two days, energy officials said.

The peak demands and the fact that natural gas reserves have not grown sufficiently since 1968 to prevent a sharp decline in production are certain to create the appearance of a catastrophic gas shortage, the official said, and probably will reignite interest in controversial energy policies, such as the deregualtion of intersate natural gas prices.

In 1974, domestic gas deliveries totaled 12,965 billion cubic feet, but last year the supply dropped to 10,844 billion cubic feet. This year, the deliveries are expected to drop another 1,000 billion cubic feet.

Some states today took unusual measures to meet natural gas needs in neighboring states.

The Southern California Gas Company, for example, offered to turn back some out-of-state gas supplies to help ease the shortage in several midwestern states that have been experience extreme cold.

The utility said its current gas supply is satisfactory because of relatively warm weather in Southern California.

The New York State Public Service Commission arranged for the transfer of eight billion cubic feet of liquified gas from the Brooklyn Union Gas Company to beleaguered upstate communities served by the Niagara Mohawk and Rochester gas companies.

New York energy officials said that several large school systems in Syracuse. Albany, Buffalo and Corning agreed to close schools following a request by the commission. The commission on Monday urgently requested all schools to close down.

However, a State Education Department official said that schools account for only 25 per cent of gas consumption in New York.

Thomas Clift. of the gas supply sectin of the Pennsylvania Public Utilities Commission, said that five-major utilities in the western part of the state have reduced deliveries to industrial users, allowing them only enough gas to keep equipment from freezing. Gov. Milton Shapp on Monday said a "state of extreme emergency" existed in Pennsylvania.

However, Clift said in a telephone interview today that all the utilities reported gas pressure had increased with slightly moderating temperatures. He added that "the danger of losing any significant number of residential users has been eliminated." Clift said that some school districts have been asked to voluntarily shut down until the weather improves.

Minnesota, meanwhile, declared an energy supply emergency because state officials fear a fuel oil shortage of up to 2 million barrels in the next 30 days if the harsh cold continues. The state ordered that thermostats be turned down to 65 degrees in daylight and 60 degrees at night. This applies to business, public institutions and even homes, though officials concede enforcement would be impossible in the last.

Portions of such major water transportation lanes as the Ohio and Mississippi rivers and the Great Lakes were clogged with ice, severely hampering ship traffic. Ice floes as high as 12 feet were reported in some parts of the Mississppi River near St. Louis. John Wild. inormation officer for the Great Guard in St. Louis. said. "Virtually nothing is moving on the river in this whole area right now."

Commercial shiping was suspended between Lake Superior and the other Great Lakes due to mounting ice and weather problems.

In another development, Amtrak suspended indefinitely eight of its train runs because of damage caused by the cold. A spokesman said water pipes have burst in passenger cars, and auxiliary steam boilers used on older trains have been failing at a high rate. In some places, watering and fueling equipment has frozen solid, water mains have broken, and track switches have frozen, he said.