Loudoun County supervisors, following the example of hundreds of towns and communities across the nation, yesterday became the first Washington area government to approve a resolution calling for a bilateral U.S.-Soviet freeze on nuclear arms production.

The resolution, proposed by Democratic Supervisor John Milton of the Catoctin District, was adopted unanimously by the eight-member board that governs the largely rural county of 60,000 west of Washington.

Milton, who represents the northern and western sections of the county, said yesterday that his resolution was prompted by similar measures passed by town meetings in New Hampshire and Vermont earlier this month. "I just decided we ought to take the ball and do it," Milton said.

"It has been a topic of much discussion lately . . . It seemed to me we're pretty close to where the message needs to go, that maybe if we could start it rolling here, we could pick up some momentum," said Milton.

Milton, whose district includes many of the county's Quakers, said the resolution makes sense in light of Loudoun's proximity to Washington, an almost certain target in a nuclear conflict.

"Nearly 60,000 Loudoun Countians live from day to day in the virtual certainty that very few of them would survive a nuclear attack aimed at D.C.," the Loudoun resolution said.

Earlier this month, in response to the New England resolutions, a Reagan administration official called the freeze idea ill-timed, a "reward to the Soviets for a massive buildup" and a penalty to the United States, which has been more restrained.

According to a spokesman for Ground Zero, a nonpartisan antinuclear organization based in Washington, the Loudoun measure was the first passed in the Washington area.