Old Man Winter lost all his road maps yesterday. It snowed in Miami. And the ice was melting in Alaska. Closer to home, the Potomac River was frozen over for only the eighth time since 1900.

The meandering jet stream in the upper atmosphere sent flurries of genuine snow on to Miami's palm trees, ending what civic boosters there called "a perfect record." It was the farthest south that snow has been reported in the United States since the record books were started in the 19th century.

It was estimated that as much as 30 per cent of Florida's orange crop would be destroyed by the cold.

In Alsaka, the weather was balmy - warmer in some spots than it was in Florida. The Anchorage Hockey Association was forced to cancel its games Tuesday when ice on the outdoor rinks melted. Temperatures there were running 20 degrees above normal.

Here in Washington, streams of people slid across the Potomac just south of Memorial Bridge, where the ice was frozen 11 inches thick.

The postmaster of Silver Spring warned residents he might curtail service if the dangerous sidewalk ice that has tripped up - and injured - dozens of his carriers is not removed.

Eduardo Gillis, 13, of 2144 Elice Ave., Oxon Hill, was killed when the sled on which he was bellywhomping crashed into a bench, causing skull fractures and internal injuries.

Three area residents were treated and released after suffering rare cases of frostbite yesterday, while water pipes in homes and businesses burst like inaugural fireworks. The National Weather Service predicted freezing temperatures will continue the rest of the week.

What's been happening, meteorologists said, is simply a reflection of the exaggerated curves in the jet stream this winter. It is dropping much farther south over the central Pacific than it usually does, then bringing warmer air much farther north to Alaska, and once again dipping much farther south over the United States with a new breath of Arctic air.

Meteorologists A.J. Wagner of the National Weather Service's long-range prediction group, said it is predicting that the pattern will continue for the next few weeks, but maintaining a prudent silence about next year. "We won't have much of an idea about next winter until we see what next fall is like," he said.

As the deep freeze continued in the mid-Atlantic states, Virginia Gov. Mills E. Godwin announced that he may declare a state of emergency and invoke sweeping executive powers to coep with the shrinking natural gas supply in the state if the bitter cold continues.

But the governor - who has asked state residents to turn their thermostats down to 65 degrees as an energy saving measure - acknowledged he does not know specifically what he would do to alleviate what could develop into a statewide crisis.

In Suffolk, for example, 2,000 workers at three major plants have been temporarily laid off because of natural gas curtailment to their employers.

In Newport News 800 city residents in 300 families were hoping that city workers can restore water service interrupted when an eight-inch water main burst because of the cold.

Maryland Gov. Marvin Mandel ordered two state National Guard helicopters aloft with medical and fuel supplies of the ice-trapped residents of Smith Island, in Tangier Sound. Another attempt to reach the hard-pressed Chesapeake Bay islanders failed when a barge loaded with fuel oil was unable to crack through the ice, which continued to clog most of the lower Chesapeake.

Mandel also asked Agriculture Secrtary-designate Bob Bergland for help in getting $20 million in federal aid to offset commerical fishing industry losses caused by the coldest winter period in memory.

The state's 7,322 licensed watermen are in an economic "crisis" because of the five-week long freeze, Mandel said.

The Artic weather eased sowmehat in the Midwest, but businesses and schools closed in many areas, from the Plains states to the East Coast. In Tennessee alone, the state's Public Service Commission estimated that 100,000 people were out of work for the day because of the lack of fuel in factories and stores.

According to the Edison Electric Institute, electric output in the 48 contiguous states broke all records for the week that ended last Saturday. The cold-weather output for the week was more than 45.4 billion kilowatt hours, 1 1/2 billion more than the previous week.

The natural gas shortage raised other alarms. The Federal Power Commission warned pipeline firms that the tremendous demand could threaten eventhe highest priority gas users - private homes, hospitals and small businesses - unless soemthing is done.

Some relief seemed in sight when Canada's National Energy Board announced in Ottawa that it has authorized emergency exports of both natural gas and fuel oil to the United States. The board said special orders have been issued allowing the export of 250 million cubic feet of natual gas a day for 60 days and a total of 50,000 barrels of heavy fuel oil during the month of January.

In the Chicago area, daytime temperatures began rising, but the National Weather Service said they would dip below zero again Saturday. Gusty winds sent fresh snows across the Dakotas and Wyoming yesterday and the new storm was spreading into Minnesota, Nebraska, Iowa and Missouri. It is expected to move east and south into the Ohio Valley, the great Lakes states and western New England land.

The temporary easing of the cold in Chicago came too late for Amtrak. Below-zero temperatures had already burst water pipes and frozen fuel facilities on Amtrak trains in the Chicago area, forcing suspensions until further notice of eight of the passenger service's daily routes. Among them was the Floridian, which provides the only rail passenger service between the Midwest and Florida, and the Shenandoah, which runs between Cincinnati and Washington, D.C.

Amtrak's "Peanut Special," however, was said to be running on schedule, carrying more than 350 friends and neighbors of Jimmy Carter from Plains, Ga., to the nation's capital for his inauguration.

Floridians were stunned by the weather that met them yesterday morning. Snowmen were built in Lakeland. Snowballs flew in Orlando and even in Frostproof. In central Florida, it was so cold at Kissimmee's Cypress Cove nudist camp that the folks there put on their clothes.

The snow flurries in Miami will be only an asterisk in the record books since they didn't fall on any of the National weather Service's recording stations in the area, but they were genuine.

The Miami News greeted it with a two-inch-high streamer headline, "Snow in Miami!" The city of Miami Beach even ordered a temporary halt to its New York newspaper ads touting the daily temperatures. It also snowed in Fort Lauderdale, Palm, Beach, Fort Myers and, yes, Freeport in the Bahamas.

The Florida cold had its grimmer aspects, too. Gov. Reubin Askew declared a state of emergency for Florida's multibillion-dollar agricultural industry. And at least two deaths in the state were blamed on cold weather accidents.

Simply getting fuel inside homes and offices has become a subject of legislative action. Sen. John Glenn (D-Ohio) introduced legislation yesterday that would shift desperately needed natural gas to the regions with shortages. The incoming Carter administration was reported to favor the bill, which is opposed by the natural gas pipeline industry.

Meanwhile, the Federal Power Commission announced on Tuesday a complicated plan to provide up to 250 million cubic feet of gas daily to Maryland and Virginia, as well as five other eastern states.

While fuel trucks were making deliveries to nearly all customers in the Washington area yesterday, they were not making them to Kevin Flynn. Flynn's 900-foot driveway at Stonehaven in Glen Echo, the mansion he rents with four other persons, has been frozen solid for more than a week, and trucks have been unable to negotiate it, he said.

"We haul in diesel oil or kerosene from the local Chevron station," said Flynn, whose home is opposite the Glen Echo Amusement Park.

"We go down there once a day and bring back two or three five-gallon cans of the stuff for the heater. But the house still gets cold. The other day the water in the dog's bowl froze," he said.