A still-secret decision to withdraw the 20-year-old Nike Hercules antiaircraft atomic warheads from Western Europe has stirred up a disagreement within the North Atlantic Treaty Organization over a timetable for making the decision public.

Some NATO officials want to make the decision, adopted last spring, public now to counteract the growing antinuclear movement in Europe.

But others, led by the United States, want to keep it secret until 1983, when the controversial American Pershing II and cruise missiles are scheduled to be deployed.

This internal NATO debate on the timing of announcing the withdrawal of the Nike Hercules warheads is part of a much broader problem facing the alliance as its nuclear modernization program has forced a full-scale reexamination of the entire 6,000-warhead nuclear stockpile in Europe.

More than 200 Nike Hercules launchers with accompanying nuclear and conventional warheads are spread in a belt that runs from the north to the south of West Germany, making them among the most visible nuclear weapon systems in that country.

Under current plans, the Nike Hercules warheads, which proved impracticable here and in the United States, where they are no longer deployed, will be replaced by the Patriot air defense system, which has nonnuclear warheads.

Word of the still-secret decision to remove the Nike Hercules was passed by NATO government officials here, in The Hague and in Rome who believe public disclosure of the move now could be a way to counter growing opposition to deployment here and in other NATO countries of the new long-range Pershing and cruise missiles.

But most NATO officials disagree with this approach, refusing to discuss the matter on the ground that it is "secret." Their reasons for keeping it secret vary, however.

Under terms of a December 1979 NATO decision, the deployment of up to 572 of the highly controversial Pershing and cruise missile systems was to be accompanied by removal of a similar number of warheads already in Europe.

When the decision was made last April to retire the Nike Hercules as a key part of this removal, most NATO countries, including the United States, wanted to delay announcement so that it could be linked directly to introduction of the Pershing and cruise missiles.

There also was hope, voiced by several NATO officials, that the Nike Hercules warheads could somehow be worked in as bargaining chips in the coming theater arms control negotiations with the Soviet Union.

Some NATO military men also wanted to hold off removing the old system until its replacement was ready.

This was true even though the Nike Hercules has never been a part of any realistic war planning, according to present and former NATO military men. Explosion of its nuclear warhead in the atmosphere, designed to counter massive enemy bomber attacks, would also blind the radars of allied aircraft and ground defense systems, according to U.S. government scientists. In addition, the problem of getting timely U.S. presidential approval to use such a weapon against attacking aircraft has never been solved.

NATO officials' old habit of overlooking the limited usefulness of many of the U.S. nuclear warheads in the European stockpile may be changing.

These days there is more talk, at least among European members of NATO, about possible opportunities to reduce the well-publicized stockpile and retire older systems such as the Nike Hercules.

For the most part, however, the Reagan administration has opposed such an approach, fearing, as one State Department official put it recently, that this could lead to "an unraveling" of all the nuclear systems.

At the April NATO meeting where it was agreed the Nike Hercules would be withdrawn, alliance officials also approved a plan to retire another old weapon, some 300 atomic demolition mines -- nuclear devices designed in the 1950s to block invasion routes.

These so-called ADMs have been stored for years in the Netherlands and West Germany. Efforts to get an agreement to plant them in German soil or even build the underground chambers from which they would be exploded have always failed.

The Nike Hercules and ADM withdrawal represent the first results of the so-called "shift study," a NATO review of the nuclear stockpile originally proposed by the Netherlands in December 1979, at the time of the alliance decision to deploy the Pershing and cruise missiles.

In hopes of getting the Dutch to agree to take 48 of the new cruise missiles, the Carter administration's defense secretary, Harold Brown, agreed that the NATO Nuclear Planning Group would undertake the study.

The Dutch government at the time saw the study as a means of getting rid of older, short-range nuclear systems designed to be used on West European soil. That step, Hague officials hoped, would be popular in their country, which had raised the biggest public protests in 1977 and 1978 over the neutron artillery shells.

In return, these Dutch officials believed, their citizens could be persuaded to accept the new longer-range cruise missiles that would be based in the Netherlands but, if used, would explode in enemy territory.

For the other NATO allies, however, the agreement to undertake the shift study was motivated solely by the need to determine which of the already deployed warheads would be replaced when the new missiles came in.

The decision to remove the Nike Hercules and the ADMs -- together totaling more than 500 warheads -- appears to fulfill the latter view of what the shift study was really about.