A record-cold Inauguration Day yesterday stranded bus riders, closed schools, burst water pipes, choked up automatic money machines, filled homeless shelters and drove President Reagan's swearing-in ceremony inside.

The temperature at National Airport sank to 4 degrees below zero -- or minus 25 degrees with the wind chill factor -- at 6 a.m. yesterday, well below the previous low for the day of 2 above, set in 1893. At least 49 deaths in 14 states were blamed on the weather, as well as one death here; at least seven cases of frostbite were treated at one area hospital.

Historic lows were recorded in cities all along the East Coast and throughout the South, as bitterly cold air swept down from Canada, and the Florida citrus crop was threatened by temperatures that dipped to 6 degrees in some areas.

The West Coast experienced a relatively balmy day, and Anchorage basked in the 20s and 30s. Akron, Ohio, and Knoxville, Tenn., were officially the coldest places in the nation, with lows of 24 degrees below zero, according to the National Weather Service. Buffalo reported 27 inches of snow and "zero visibility," and only emergency vehicles were allowed on the streets.

In Washington, more than 1,200 homeless persons took refuge in private and city-run shelters Sunday night, filling some to capacity.

A 61-year-old man, identified as Leander V. Gilmore, of no fixed address, was found dead in an abandoned house in Southeast, apparently a victim of exposure, according to D.C. police.

"This is no time to be outside, not with these temperatures," said Maurice Todd, 24, a coordinator at the Blair School shelter at 611 I St. NE, where about 80 men dozed or talked quietly in a crowded room yesterday afternoon.

Relief of sorts is in sight today; highs were expected to reach about 25. Forecasters said it would be sunny but windy, according to National Weather Service spokesman Bob Oszajca.

Yesterday's high of 16 degrees was reached between 3 and 4 p.m. When the president was sworn in at noon inside the Capitol rotunda, the temperature was 7 degrees, well below the previous inaugural temperature low of 16 degrees that greeted President Ulysses S. Grant at noon in March of 1873.

The inaugural holiday and the historic cancellation of the parade to the White House kept highway traffic and subway ridership mercifully light, but that did not prevent confusion and disruption.

Traffic signals throughout the city were blinking to their own untimed rhythms, or not at all, and some drivers took the opportunity to ignore red lights in general.

Cars stalled throughout the area, and the 42 emergency phone lines at the Automobile Association of America were jammed all day. Callers were put on hold for 20 to 30 minutes, and the wait for a tow was measured in hours, said one AAA worker.

"There are not enough phone lines and tow trucks in the world to cope with weather like this," said Mary Anne Reynolds, a AAA spokeswoman. By midnight last night, a beefed up AAA staff working in a room half the size of a football field had taken 3,006 calls, most for dead batteries and cars stalled with frozen gas lines, Reynolds said.

The Metro subway system experienced some delays, but all lines were running at a fairly even level, said Metro spokeswoman Beverly Silverberg.

Bus riders, on the other hand, in some cases had to wait for replacement vehicles on heatless buses when heaters went out on at least 35 of some 250 buses Metro had on the road, Silverberg said. But ridership on the system was lighter than on most holidays, she added.

Pepco and Virginia Power Co. (formerly Vepco) both reported that peak-use of power reached historic highs yesterday around the Washington area. Both companies also reported scattered power outages that they said had not caused major problems. Virginia Power Co. officials asked customers to voluntarily cut their power use to avoid an overload of the system.

The phone lines of the Mayor's Command Center were jammed much of the day with calls from more than 400 District residents facing the record cold without heat and more than 250 saying they did not have water because of broken or frozen pipes.

Joseph Yeldell, director of emergency preparedness, said the center is not responsible for fixing broken lines or repairing heating problems, but would contact the building owners and report the problems.

"The calls keep coming in, and I don't know when we will be able to catch up with the backload we already have," Yeldell said, despite a larger-than-normal staff that will work through the night.

Meanwhile, Jeanette Millhouse sat in her one-bedroom apartment on Kendall Street NE with sheets of ice covering the walls and doors, in spite of an electric heater and kitchen stove burning continuously to heat the apartment.

She declined an electric heater offered by the city because she feared overloading the electrical system. "I sure hope someone comes and helps us before we freeze to death," she said.

Amtrak experienced delays of up to two hours in the Northeast corridor yesterday morning because switches froze, a spokesman said. By evening, however, the trains were back on schedule, he said.

On one Northwest Airlines flight to Seattle from National Airport yesterday morning, the frigid weather knocked out the auxiliary power unit used to heat airplane cabins. After a 45-minute delay, the engines started, but the water in the lavatories and coffee pots remained frozen. Passengers kept their coats on for most of the flight before landing in the welcome Seattle warmth of near 40 degrees.

Over the weekend, First American Bank of Virginia had to send out squads of maintenance crews with hair dryers to thaw outdoor Money Exchange machines. By yesterday morning, the machines were all back in service, said bank vice president Jean Segner. While Virginia banks were open yesterday, District banks were not, and in some cases, customers trying to use electronic tellers in the city went away empty-handed.

City traffic crews were out trying to fix some 100 broken signals. To minimize the problem today, the lights were to be kept on their morning rush hour settings last night, a public works department spokesman said.

Water mains tend to break at the end of cold spells because it takes time for the freeze to set in, so the city expects more problems with old water mains today, said William McGuirk, a department official.

Area plumbers were swamped with calls from homeowners with broken pipes, and fuel oil distributors did a booming business.

Despite the extreme cold, two of the city's major shelters for the homeless were less than full. The Blair School shelter, with 150 beds, recorded 107 tenants Sunday, and the nearby Pierce School shelter, also with 150 beds, recorded 136.

Supervisors at the two city-run shelters attributed the vacancies to the fact that a much larger shelter operated by the Community for Creative Non-Violence at 2nd and D streets NW is closer to downtown, where many of the city's homeless wander during the day.

At the CCNV shelter, a three-story former Federal City College building that has held as many as 985 persons in recent weeks, 810 homeless persons were counted Sunday night. In a quick action by the Pentagon and the Department of Health and Human Services, an Army van brought in 340 blankets at 4 a.m. yesterday, according to CCNV activist Mitch Snyder.

An air of restrained bedlam hung over the shelter, as men in overcoats talked loudly over blaring radios. Others played cards, dozed in chairs or on the concrete floor.

The showers at Pierce shelter were frozen, obviating the required nightly shower for all tenants at the shelter. "Some of the guys will be glad for that," said Prince.

There was some humor to be found in the frigid capital yesterday, provided by a lawmaker whose home state is famous for its icy climate. Sen. David F. Durenberger (R-Minn.) inserted into the Congressional Record a tongue-in-cheek denial of speculation that today's weather was, as he put it, "Minnesota's revenge" for the election results.

Former vice president Walter Mondale carried his home state, and Durenberger noted that when asked what he wanted for Christmas, President Reagan had replied "Minnesota."

Today, the senator said, "he got his wish."