Icy winds were swirling along New York's East River last November when Joe Fino, a young Air Force veteran, left his $9-an-hour job as a stock clerk to seek his fortune in the softer breezes of California.

He blew his savings on a plane ticket and spent half of his remaining $30 for a taxi ride from the airport to downtown Los Angeles. He barely missed a passing grade on an oral examination for police recruits, failed at a few other job attempts and then found his energy flagging.

He has not had a regular job since, saying he has found it more convenient to move among a series of free public shelters scattered about the area than to apply for welfare. Fino has joined a group of people who have made much of urban America the focus of a problem that after two years of intense media and government attention still defies solution. The problem is homelessness.

For every social ill, there was once thought to be a government solution, and past administrations stepped off boldly to prove just that. But homelessness is different. It has become something of a metaphor for the clash that has occurred since 1981 between the Great Society and the Reagan revolution.

Homelessness has defied not just solution but also definition. In the process, the issue has revealed the prevailing American ambivalence toward federal government solutions to social problems.

Homelessness is a deeply personal problem for those on the streets. It is also an example of government in action -- groping with good intentions but confounded by inadequate knowledge and conflicting theories about government's proper role.

Did government, through the economic policies of the Reagan administration, help increase the number of homeless people in America today? Can government, in the absence of solid information about the scope of the problem or its causes, solve the problem? Is there a problem?

Just the effort to count the homeless and get some fix on the source of their misery has generated enough paper, in the form of government reports and academic studies, to keep a trash-can fire going for weeks. Most agree that Los Angeles, with an estimated 35,000 homeless, may have more street people than any other U.S. metropolitan area. But there is little agreement on how many there are nationwide, much less how to help them.

Last year's campaign debates over the issue have subsided, but in hundreds of cities nationwide the homeless are still a constant political irritant.

Homeless-advocate Mitch Snyder's struggle to win federal money for an 800-bed shelter in the District of Columbia, although one of the more important and bitter confrontations, is only one of many. Los Angeles supervisors face an unexpected budget deficit because of new demands for general relief for the homeless. Austin, Tex., is embroiled in controversy over the Salvation Army's plan for a new 200-bed facility for transients on commercially fashionable Sixth Street. Many cities are anticipating a new round of demonstrations by street people creating makeshift homeless villages when winter descends. Government Seems Powerless

Congress, controlled in part by Democrats, and the Republican White House have appeared powerless to solve the problem, even in a time of rising employment and economic health. That may stem from several causes, the complexity of which have become clearer the more the issue has been studied.

The federal effort to count the homeless, or at least provide a more verifiable estimate than the 2 million figure often used in stories about homelessness, has produced such a divisive political and legal donnybrook that all professional efforts to count the homeless have ceased.

In the absence of useful statistics, legislators have been torn over how much to appropriate to try to help. Rep. Mary Rose Oakar (D-Ohio) became so frustrated over this debate last year that she picked a figure of $62 million for a proposed demonstration project for mentally ill homeless because it happened to match the amount the House had raised military aid to El Salvador that day.

Most homeless shelters are privately run, by churches or other charitable groups. Although much of their funding comes from federal and local governments, those who operate the shelters and many social welfare experts insist that only such private volunteers have sufficient desire, experience and flexibility to help people with so many difficult problems.

Many of the root causes of homelessness -- such as mental illness, urban renewal and the sexual revolution -- resist bureaucratic solution and are shunned by politicians as being too difficult or delicate to address.

Interviews with homeless people indicate that many have rejected the government programs available to them and have chosen to move from shelter to street to shelter as the simplest approach to their problems. Although often miserable, they express a desire to extricate themselves with as little outside help and guidance as possible.

President Reagan was ridiculed early last year when he said many people are homeless "by choice." But the homeless do make choices, although often they must choose between unattractive alternatives, such as welfare or charity, and sometimes make decisions that seem rational only to them.

Isaac Rim Jr., 33, a former $4.50-an-hour nurses' aide, said he has been on the streets 11 years. "I like it," he said simply.

Rim stopped briefly as he headed toward a church-run library for derelicts in downtown Los Angeles, a copy of "The Science of the Mind" by Ernest Holmes under one arm. "I got my freedom," he said. "I got my independence. I work when I want to work." A Shifting Population -----

Nearly every study done in the last two years has suggested that for most people, homelessness is a temporary condition. Of the 20 homeless individuals interviewed at length in and near Pasadena's Depot, a barren shelter in the basement of a local church, only seven might be considered likely candidates for the semipermanent underclass of derelicts -- the alcoholics, mentally ill and illegal immigrants who have always lived on the edge of American society.

If most of these 20 did not seem to be permanently homeless, neither was a night in a shelter a new experience for them. For as many different reasons as they had different names, parents, family ties and talents, the people passing through the Depot had decided, with government programs available in nearly every case, to suffer the discomfort of life on the street.

"My big problem is I can't stay in one place too long. I get bored and I want to see something else," said Richard Brightman, 45, a carpenter and horse handler who had arrived from Las Vegas two weeks before.

"I knew it was going to be temporary for me. I didn't feel no remorse, no regret, no dissatisfaction," said Michael Gunther, 33, who said his time at the shelter helped him prepare for his electrical engineering exams at Pasadena Community College. A misunderstanding, he said, had forced him out of his room at a friend's house. He needed a bed only briefly before finding another cheap rental. "I'm a man. I'm going to take care of myself one way or another."

One shelter veteran in downtown Los Angeles took this attitude to its light-hearted, or insane, extremes: "I don't have to be here. This is just a vacation for me."

Nearly every expert on the homeless assumes, with little hard data, that the current mass of homeless people is on average younger and includes a larger proportion of women and minorities than the skid row population of 20 years ago. Many experts have suggested that the latest people on the streets are different because they are victims of new social forces and thus require more and better government services than have been provided to derelicts in the past.

"Whether the homeless person is someone recently unemployed, someone existing on inadequate public assistance or SSI [Supplemental Security Income] benefits, someone who is mentally or emotionally impaired, it all comes back to economics," Katharine W. LeVeque, president of the Greater Baltimore Shelter Network, told a congressional hearing. "The greed and insensitivity of those who control our economic lives are responsible." Searching for Reasons ----

Some experts argue that the new homeless are the result of Reagan's budget cuts or the shift from smokestack to electronics industries and are helpless.

Los Angeles Deputy Mayor Grace Davis, on the other hand, said she believes that her city has become attractive to the homeless because "we have a more generous welfare system than in other states."

Vicki Baggette of the United Way Inc. office here said charity workers think the growing numbers of homeless appearing at shelters may have as much to do with publicity, attracting people who would have found shelter elsewhere, as with any increased economic distress.

Many homeless people blame their troubles on themselves.

"I don't manage money too well, put my priorities in the proper order," said Jerome Brown, a messenger and accounting clerk who does temporary office work. When the flu kept him home one week, he found that he was left with too little savings to pay the rent. The money had gone "in the streets . . . just having fun, having a good time . . . entertaining women, keeping up with my buddies . . . . If I'm making $960 a month, I usually spend at least $250 on marijuana."

Some analysts think the unpredictable nature of comments from the homeless may have kept many advocates of the homeless from probing the ideas and needs of their derelict constituents as closely as they should, and help explain the confusion over how the government can best help.

Anna Kondratas, who recently completed a long report on homelessness for the Heritage Foundation, said she found two distinct groups of homeless advocates: individuals who have been working on skid row for years and "do not see it as a political thing," and "highly motivated activists," more recently arrived, who have taken up the cause of the homeless and "put it in the context of their long-held political beliefs."

The feeling persists, among some experts as well as the homeless themselves, that many derelicts appearing at local shelters are beyond help. For one thing, the federal courts have ruled that harmless individuals, no matter how self-deluded, may refuse government help, counseling and hospitalization if they choose.

For another, existing shelters, despite the meager federal and private funds they receive, seem to have provided enough of a refuge to discourage some homeless from seeking further help or training. A UCLA research team, for instance, found that most of a group of 94 homeless men it interviewed rated their food, sleep, shelter, safety, hygiene and clothing as adequate, even though they all said they disliked life on the streets.

The older, more self-sufficient homeless who see shelters as temporary expedients complain in particular about other derelicts who seem too comfortable with their lot. Ed Simmons, a 56-year-old former sales executive who says he once made $35,000 a year, was waiting for an appointment with a state employment counselor when he pointed out a stocky Depot resident, a veteran of several other shelters.

"He doesn't want to work," Simmons said, "and he's taking everything he can get, any way that he can get it. And he's doing just fine. He's doing much better than I am."

Brightman, annoyed at being without his carpentry tools, said, "I notice there's a lot of these people that don't really care. They just take advantage of every situation, something they get for nothing."

"Many of them have self-destructive tendencies, like I have," said Mahei Saeed, 54, a former teletype operator. "There is bad management, because I know people who just splurge their money . . . . My feeling is, the only thing to be done about the homeless situation is to reach these people before they become unreachable, because these people who've been out on their own for two or three months, for five months, they are far gone, we cannot reach them."

NEXT: Counting the homeless.