President Reagan and Soviet leader Mikhail Gorbachev were all smiles at the Moscow summit as they signed documents putting into force a treaty to ban intermediate range nuclear missiles.

But some people directly affected by the INF treaty are not smiling quite so broadly.They see a gargantuan task ahead as the superpowers - for the first time in the atomic age - systematically destroy an entire class of nuclear weapons, each under the suspicious stare of the other.

Executives at the Hercules Inc. defense firm wish their company had been spared the honor of selection by Moscow to host 30 Soviet treaty inspectors for 13 years at a Magna, Utah, missile plant. The last thing a U.S. defense company looks forward to is a bunch of Russians snooping around.

Soviet defense installations likewise will have to get used to American inspectors. Both Soviet and American "gamekeepers" are preparing to spend years in alien environments under constant scrutiny themselves by domestic security men.

Top officials of America's new On-Site Inspection Agency, which oversees treaty implementation, are bracing for 16-hour days coping with a torrent of technical details as they check and doublecheck missiles and their myriad components.

"We're lean and mean and getting meaner as the countdown comes," joked Navy Cmdr. Kenneth Pease, a spokesman for the agency, who has been hard at work since March.

The countdown he referred to is a work-packed 90-day schedule paving the way for destruction of 2,400 missiles.

An unprecedented system of intrusive "verification" to prevent cheating on the treaty will be established.

New exchanges of missile data must be completed and inspection teams readied within a month. Then, during the next 60 days, initial "baseline" inspections must be carried out at 133 weapons sites in the Soviet Union and Eastern Europe and 26 sites in American and Western Europe.

Meanwhile, treaty inspectors will set up their operations at Hercules's Magna, Utah, missile plant near Salt Lake City and at Votkinsk. The monitors will begin tracking what goes in and out the factory gates - a safeguard against illicit missile production.

"We don't feel honored," said Hercules's vice president for public relations Donald Kirtley in an interview with Reuters, referring to Moscow's selection of his firm for so-called "portal inspection" - monitoring at the plant gate.

Edward Sheehy, president of the firm's aerospace division, recently told a Washington Post reporter: "Obviously, we would prefer that the Russians weren't there. We were not consulted . . . (jut) simply told the Russians had picked us . . . We got nailed."

Hercules is one of the world's biggest missile makers.

The Utah plant builds parts for MX, Trident, and Midgetman nuclear missiles, which are not covered by the INF pact. Nevertheless, shipments of these weapons systems would be subject to inspection because their containers might theoretically hold banned INF components.

The chance to keep tabs on MX, Trident, and Midgetman was surely the reason Moscow selected the Hercules plant for monitoring, Kirtley said.

He said Hercules supported the INF treaty, stating, "We believe that arms reduction is an important consideration on the planet today."

But he said there had been concern that the firm could lose out on government defense contracts because 30 Russian monitors were entitled to inspect any large shipment in or out of the plant.

The Pentagon has issued an orders barring discrimination against the firm in awarding military contracts.

Hercules is also worried about safeguarding key trade secrets such as its formula for tough, ultralight "graphite composite" material.

"We're examining whatever other (security) measures we'll need to take because there will be 30 trained inspectors nearby," Kirtley said.

The National Security Agency, which oversees electronic espionage, has promised to safegaurd Hercules' computers and communications network against Soviet snooping, officials say.

Life will not be free and easy for the 30 Soviet inspectors who will live in a special compound near Magna, 15 miles from Salt Lake City, according to Pease.

"The Soviets will be escorted 100 percent of the time that they are here in the United States (except) when they're in their living quarters," he said.