Haunted by the terrors of the Iran-contra affair, the White House has issued a confidential memorandum forbidding any discussion by administration officials of ''private or third party'' aid for the abandoned Nicaraguan anticommunist guerrillas.

The gag rule was signed Feb. 10 by two senior presidential aides: Chief of Staff Howard Baker and National Security Adviser Colin L. Powell. Broadened at Democratic insistence to include Cabinet members as well as White House staffers, it contains not a single loophole.

Once House Democrats defeated President Reagan's contra aid package on Feb. 3, chances for armed resistance against Nicaragua's Sandinista regime were bleak at best. Those anemic prospects are further reduced by the White House gag.

The order was strongly supported by House Democrats who have fought Ronald Reagan's Central America policy for seven years. When they first read the ''Memorandum for the White House and NSC Staff'' last week, these contra-haters succeeded in widening its impact. Rep. David E. Bonior, the chief deputy majority whip and a longtime apologist for the Sandinistas, was in the lead, insisting that the memo be sent to all Cabinet members.

One immediate result: a tough pro-contra speech that Education Secretary William Bennett intended to give on Feb. 29, the day all contra aid must cease, probably will have to be reworked.

Bennett is not the only Cabinet member unhappy with the memo. Surprisingly, Secretary of State George Shultz, has taken a tougher pro-contra line than the White House since the Reagan aid program was defeated in the House.

Although Shultz told his own aides before he was aware of the Baker-Powell edict that they should not ''solicit'' private contra funding, he left a loophole prohibited by the gag rule. ''If someone comes to you and asks, 'can I give money to the contras?' tell him: of course,'' Shultz had said.

With the Iran-contra scandals in the background, the Baker-Powell memorandum does assert that the president will ''continue to work through the Congress to secure the necessary aid for the freedom fighters.'' Such chances are not bright. As for further help to save the resistance, the memo does not pussyfoot, saying ''no administration official should take a position for or against private support.''

Any privately raised funds sent to the administration must be returned forthwith, the memo says. Officials must ''discourage private individuals from discussing private aid during briefings and meetings'' attended by administration aides.

The White House memorandum is predicated on this thesis: No matter how ''well-intentioned'' private or third-party aid (from Israel or Saudi Arabia, for example) may be, it would be ''misunderstood, misinterpreted and, therefore, counterproductive.'' Although the memorandum does not say so, its obvious purpose is to avoid the taint of Iran-contra.

Intended or not, the gag rule reinforces the judgment of pro-contra pessimists in the administration and Congress who on the day after the Feb. 3 cutoff vote privately predicted the early end of armed resistance. What the White House memo does to a future ''Who lost Nicaragua?'' debate is unclear. Republicans are eager to launch such a national political inquest if the current peace plan fails to bring democracy to Nicaragua.

To blunt the Republican assault and protect House Democrats, Speaker Jim Wright, Majority Whip Tony Coelho and Bonior are pressing a small new package of nonlethal aid to the contras. The pro-contra bloc, angered by the White House gag, will oppose this and press for arms aid.

The possibility that third-party aid would save the contras always was dubious at best. But when the president's men insensibly join David Bonior in putting the final nail in the contra coffin, the Reagan Doctrine has come full circle.