Mayor Marion Barry sat casually in the back seat as his chauffeured black sedan rambled along the streets of northwest Washington yesterday to the clumpety-clump accompaniment of the tire chains on the rear wheels.

Barry stared straight ahead. He rarely looked down the occasional snow-clogged side streets. He appeared to hardly notice the truck in front whose rear end wigwagged in the slippery slush. He did not glance at the occasional pedestrians who lined up at downtown street corners to tiptoe along the narrow footpaths through the banks of snow.

The mayor is not dealing wih this snow problem personally. He said he is confident that the chore is being capably handled by his two righthand men -- city administrator Elijah B. Rogers and general assistant Ivanhoe Donaldson. It is not a job for the city's elected leader.

"What's to lead? It's not a crisis," Barry said. "That's why you've got all these staff people around. "There are more important things for me to worry about than snow -- housing, (the) supplemental budget. When you have a good team, you don't have to get involved in everything.

That's what wears the mayor out.

"If people got as excited about the housing problem and about unemployment as they did about snow, maybe we'd get something done. This is going to go away in some days."

Would city crews shovel the snowbanks from around street corners? a reporter asked.

"What's the purpose of shoveling the corners? Are you gonna pay for it?" was Barry's response.

Will the snow be hauled away? "I don't know," said the mayor. "Where are you going to put it?"

What about the people who could not dig out their cars, or tried digging once only to have the cars plowed back in? the mayor was asked. How would they get to work?

"Take a bus," he said gruffly.

The buses were not running in the morning.

"They can walk."

"To be a nonsnow-oriented town, I think the city has done a fantasic job," Barry said. "Look at how clean those streets are," he said as his sedan passed near 34th and Highland streets NW. "They haven't been that clean in three years."

Then the car passed a street where vehicle treads had packed down the snow in two narrow paths and apparently no plowing had been done. "There must be 5,000 streets in the Disttrict of Columbia," Barry said as the snow-clogged road was pointed out. "You can't clean them all."

The city's chief executive missed many of the problems city and area residents have been coping with since late Sunday.

Barry was in Miami on a four-day vacation until Tuesday morning. He has not shoveled the snow from around his 1971 Volvo, he said, because he does not have to use the car. The streets in front of his house on the 1200 block of E Street NE has been plowed. The mayor said he did shovel a path from the door of his house to the street.

City trucks have hauled away much of the snow from the sidewalks surrounding the District Building, which yesterday housed only a skeleton staff. Many of the telephone calls coming into the mayor's office about snow-related problems were being referred to mayoral aides or to the city's emergency preparedness center.

Even some looting that broke out Tuesday on Capitol Hill after many persons who turned up to apply for $5-an-hour jobs shoveling snow for Metro found out all the jobs had been taken, did not worry Barry.

"I've learned that wherever there's a shopping center or place where goods are sold, you will have some people who will take advantage of the situation. The same thing would have happened if there had been a blackout," Barry said.

"That's minor compared to what could have happened. To me, it's nothing to get worried about," he said. "Three times as many people showed up as they had intended, which shows up the need for more money."

During an appearance yesterday on the WTTG-TV noontime program "Panorama," Barry cited the snow removal operation as a barometer of the change he has made in the delivery of city services during his seven weeks in office.

"I think the snow situation is the best example of change in attitudes," he said. "More people have called the office to indicate that the side streets have been plowed for the first time."

While on the show, Barry catalogued the successes of his first days in office and also sampled flame-fried venison, quail meat and buffalo steak. It's a little tough," Barry said of the buffalo steak. "But not as tough as running the city."