Harmon Dunathan's concern that America's colleges were failing to educate its students about the facts of nuclear war were brought home when he saw "Nuke Iran" signs on his upstate New York campus during the hostage crisis.

"It was the first time I'd seen 'to nuke' as a verb form," Dunathan said in a telephone interview the other day. "I realized these relatively naive 18-year-olds didn't know anything about nuclear weapons."

So Dunathan, a 49-year-old biochemist and provost of Hobart and William Smith Colleges in Geneva, N.Y., said he began a campaign to get universities to teach students about nuclear war.

Dunathan said he's talking about a middle-of-the-road position, not a radical political stand. But it hasn't been easy, he said, because the higher education establishment isn't comfortable with the issue. "They're a little bit afraid of the issue," he said. "They don't want it to get mixed up with their financial aid problems. That was said to me very bluntly."

College lobbying groups united for the first time this year to fight the Reagan administration's proposed cuts in student financial aid, but the groups are known for their reluctance to take stands on political issues.

Thomas Stauffer of the American Council on Education, a college umbrella group, and the president of another college association are scheduled to join Dunathan at a press briefing on the nuclear war issue today at the Arms Control Association, a nonprofit educational group.

Stauffer said there seems to be "a national groundswell of interest" in nuclear weapons that he hasn't seen since the aftermath of the Cuban missile crisis nearly 20 years ago. A vocal minority of college students has demanded to hear more about the issue, he said, so ACE cosponsored a recent symposium on nuclear matters.

The symposium, which Dunathan organized with foundation money, drew faculty and administrators from 75 campuses. It was designed to explore ways colleges could include nuclear arms studies in their curricula, Dunathan said.

Marsha McGraw, associate director of the Arms Control Association, said one speaker noted that a recent survey found that only 7 percent of undergraduate and 11.5 percent of graduate schools offered such courses. She added that her group has received 175 requests for information from students and teachers in the last year, a great increase from previous years.

Stauffer, McGraw and Dunathan agree that the recent interest in nuclear issues seems driven by "loose talk" about nuclear war by Reagan administration officials.

Gauging the depth of the campus interest is more difficult, however. A weekend meeting in Philadelphia of student leaders from 50 major universities, for instance, didn't even include the nuclear arms debate on its agenda of workshops, which ranged from financial aid lobbying to gay rights on campus.