A grass-roots campaign to freeze nuclear armaments is building across the country - with a breadth of interest comparable to the antiwar movement of the 1960s.
Evidence that the 16-month-old ''freeze campaign'' continues to gain strength comes from many areas of the nation:
* In Vermont March 2, voters at town meetings in 143 of the state's 246 cities and towns approved a measure calling for ''a mutual freeze'' in the United States and the Soviet Union ''on the testing, production, and deployment of nuclear weapons . . . with verifiable safeguards satisfactory to both sides.''
* In Washington, a measure calling for a weapons freeze followed by major force reductions and stabilizing measures will be introduced into both houses of Congress March 10. Sponsored by six senators and over 50 members of the House, it marks a major bipartisan step in the campaign.
* In California, recent polls show that voters approve a bilateral freeze by a 2-to-1 margin. Supporters have already gathered 450,000 signatures - more than enough to put the measure on next November's ballot.
* In Boston, 200 professional musicians protesting the nuclear arms race crowded onto the stage in Symphony Hall Feb. 21. Their concert of classical music featured a song cycle by Harvard professor and composer Earl Kim, who flew over Nagasaki 24 hours after the atom bomb was dropped in 1945. The concert brought messages of support from as far away as the Japan Philharmonic Orchestra and grossed upwards of $77,000 for its sponsors - much of which went to support the town meeting campaigns in northern New England.
The freeze movement, which draws strongly upon religious groups like the American Friends Service Committee, is becoming increasingly well organized. Last January the Nuclear Weapons Freeze Campaign National Clearing House was set up in St. Louis. Co-director Karin Fierke claims to have 17,000 to 20,000 people ''actively organizing'' in grass-roots efforts around the country designed to influence public officials. Its second national conference in Denver in mid-February drew 450 people and garnered national television news coverage.
She is encouraged by the results. She reports ''some level of freeze activity'' in 279 congressional districts in 43 states. In addition, she says, resolutions approving a weapons freeze have passed the legislatures in Massachusetts and Oregon, the New York State assembly, and the House of Representatives in Wisconsin and Connecticut. And more than 50 organizations, including the National Council of Churches and the YWCA, support the campaign.
But so far, says Jeffrey Porro of the pro-freeze Arms Control Association, there is little evidence that the movement has influenced administration policymakers. To be effective, he says, the campaign ''has to go beyond the usual liberal constituencies'' of Hollywood stars and university academicians and ''extend to people who usually are not committed on these issues.'' He sees that coming, however, and notes that his group is increasingly receiving requests for speakers from Midwestern communities.
Officially, the strategy of the campaign is to persuade Congress to adopt a resolution freezing nuclear arms within two to five years. Some organizers, however, feel the movement is developing so rapidly that a congressional vote could come even sooner.
Robert Alpern, director of the Washington office of the Unitarian Universalist Association and chairman of the Government Relations Task Force of the Nuclear Freeze Campaign, says he thinks a favorable vote could come within 18 months. He notes that congressmen have taken note of the groundswell across the country - and of the large European demonstrations against nuclear armaments last fall in Bonn, London, Paris, and even Bucharest. Although the European movement has been less visible since the declaration of martial law in Poland Dec. 13, observers expect an upsurge of activity come spring.
The freeze campaign, drawing support not only from serious students of arms control but from a broad spectrum of pacificists, environmentalists, and those opposed to President Reagan's defense budget, has recently had most of the attention. Spokesmen against it are harder to find.
Eugene V. Rostow, head of the US Arms Control and Disarmament Agency, recently told the 40-nation Committee on Disarmament in Geneva that ''under present circumstances'' a ban on nuclear weapons tests would not help to ''reduce the threat of nuclear weapons or maintain the stability of the nuclear balance.''
And Prof. Thomas Schelling of the Kennedy School of Government notes that the arguments are identical to those raised in the early 1960s - when, he said, there were ''plenty of maps with concentric circles'' showing the extent of nuclear destruction from a single bomb. He says the campaign is ''totally diverting attention from what ought to be under discussion'': a sensible long-range nuclear program, and ways to limit and stop a nuclear war if it starts.
Part of the publicity problem lies in new White House security clearance procedures. Requests for telephone interviews by this writer were so delayed that White House staffers, who were apparently willing to talk, were unable to get permission to do so before this story went to press.