Duncan Fraser had a dream: to attend Princeton University this fall. With near-perfect college board scores, National Merit and Presidential scholarships, the dream seemed tantalizingly close.

But last spring Duncan, then a high school senior from Decatur, Ga., was informed that he was ineligible for federal aid. It appeared that his parents would have to mortgage their home to afford the $13,000 cost of sending him to Princeton for one year.

"My parents have worked very hard, and I don't think I can ask them to live in poverty so I can live out my expensive dream," he said.

So Duncan will enroll this fall at North Carolina's Davidson College. It gave him a full scholarship.

College administrators say that Duncan's story is being repeated around the country. The Reagan administration's cuts in student aid are only beginning to take effect, but administrators warn that they already have had a stinging psychological impact.

"It's mostly anticipation," said William McNamara of the National Association of Independent Colleges and Universities. "The uncertainties about financial aid really influenced kids. A lot decided to go to public colleges, or to go to two-year colleges or to delay college."

In particular, college officials are concerned by signs that poor or minority students are counting themselves out. Admissions officers report that the students who will be freshmen at private universities this fall are less the T and more the alligator shirt crowd.

The changes so far are slight, although officials fear they are omens of trends to come.

At Harvard College, the number of black applicants, the number of applicants from public schools and the number of applicants who requested financial aid all dropped slightly this year, according to William R. Fitzsimmons, director of admissions. The number of applicants to Harvard whose parents did not attend college is down one-third from three years ago.

Also troubling Harvard officials is a drop in the number who decided to come after being admitted. This drop was especially pronounced among black students, and 41 percent of the admitted blacks who went elsewhere said finances were a primary reason. Among whites, only half that proportion blamed finances for going elsewhere.

The total annual cost of attending Harvard is more than $13,000. However, 40 percent of the class receives scholarships worth an average of $5,600, plus loans and jobs worth an average of $3,000.

John Phillips, president of the National Association of Independent Colleges and Universities, warned in a recent speech that admissions officers around the country are noticing changes in the kind of people who apply to independent colleges.

"They began to see an alarming change in the economic portrait of the applicant pool," Phillips said. "Many colleges reported fewer applicants from families in financial need and from families not previously exposed to higher education," he said.

Administrators admit that they are responsible for part of the problem, by raising a big stir over the administration's proposed cutbacks in student aid. Many students, unaware that Congress had rejected some of the administration's proposals, assumed they would never qualify for aid.

"We intended to generate as much publicity as possible," said Michael Hooker, president of Bennington College, "but we were too successful. There was an unwarranted hysteria among parents and students. That's not to say the fears won't be warranted this time next year."

While some officials worry that the student aid cuts threaten the survival of some private colleges, those with national reputations -- and those that cater to students from the wealthiest families -- do not seem in trouble.

Bennington College, in Vermont, is the most expensive college in the country, costing more than $14,000 this year when personal expenses are added to the bill, yet Hooker said the number of applications rose this year.

The recent cuts in student aid include the following:

* The annual maximum for Pell grants, the basic federal scholarships awarded on the basis of need, will be cut from $1,800 to $1,674 unless more money is added to the program.

* Funding for supplemental grants was cut 26 percent from last year's level.

* College work-study, national direct student loans and state student incentive grants were all cut about 4 percent.

* Students entering college this fall no longer will be eligible for Social Security education benefits, which now constitute one-fifth of student aid.

* Guaranteed student loans, which formerly were available to all students regardless of need, now are limited to families with incomes of less than $30,000 or those with higher incomes who can demonstrate need.

Many students have not realized that they may be eligible for loans even though their family income is more than $30,000, administrators say. The number of loan applications is down 30 percent from last year, according to Education Department figures, although there may be a surge this month and next.

The cuts come at a time when college fees are rising about 15 percent a year, according to the National Association of of Student Financial Aid Administrators. Many officials are worried that the Reagan administration will press for deeper cuts in student aid next year.

Ironically, community colleges are now booming. Rosemary Wohlers of the American Association of Community and Junior Colleges said that enrollment at community and junior colleges is expected to rise 4 percent. Such institutions are popular because they are cheap and focus on job training, while permitting students to hold jobs while attending college part-time.

This growth is coming partly at the expense of four-year colleges, however -- a record number of students are transferring from universities to community colleges. Four-year colleges are finding that they must scramble for students, and lure them with attractive financial aid packages, to maintain enrollments without lowering their admissions standards.

This is particularly so because the end of the baby boom generation now is trickling through universities and the number of college-aged people will decline by 20 percent over the next 15 years. To avoid losing too much ground, colleges will have compete more vigorously with one another.

In the wake of the cuts in federal aid for students, universities already have demonstrated some ingenuity:

* Seattle University has doubled its summer jobs program and provided a "tuition work bank" in which the university will add a large premium for earnings invested toward tuition costs.

* The University of Northern Colorado has launched a program that will allow students to work off their school bills during the year.

* Bennington College is exploring the idea of subsidizing loans that needy parents get from commercial banks.

* The University of Delaware is expanding a computerized scholarship search that allows students to look for obscure scholarships tailored to their circumstances.

Some states are also moving to help financially-strapped universities. Colorado has begun a matching fund, offering to match contributions to colleges dollar-for-dollar up to a limit.

Educators in a few states are considering a proposal rejected by the Massachusetts legislature that would impose a tax on cigarettes or alcohol to finance student aid.

Seven states have passed legislation allowing colleges to issue tax-exempt bonds to raise money for student aid. Purchasers of the bonds do not pay tax on the interest, and so the interest rate is low.

Therefore, colleges can issue bonds and pay only about 10 percent interest on the money, while re-lending the funds to parents at a slightly higher interest rate -- still well below market rates -- to cover handling expenses and the risk of default.

Dartmouth College pioneered this scheme, and enabling legislation has been passed in Connecticut, Florida, Illinois, Iowa, New Hampshire, Maryland and Massachusetts. James J. Unland, director of public finance for William Blair & Co., the Chicago-based investment banking firm that developed the program, said that he has had inquiries from about 20 other states.

The irony is that these bonds, which were developed because of the cuts in federal aid, will cost the federal government because the Treasury does not collect taxes on these bond earnings.

"There is no way the private capital market can do what Uncle Sam can do," Unland cautioned. "The best this program can do is be an important supplement to federal programs."