While many Arlingtonians may have been sipping Bloody Marys and muttering thickly about the hair of the dog yesterday morning, their County Board was on the job.

Looking impossibly fresh at 11 a.m., the five members of the board renewed an Arlington tradition: The New Year's Day meeting.

"People ask me from time to time, why is Arlington different?" said John D. Milliken, who until yesterday was the County Board chairman. "One of the things that's different is that it's a citizenry that can get up early on New Year's Day."

Oblivious to the probable dissent of those still slumbering, the 30 citizens in the audience roared with laughter.

The business of the day, largely ceremonial, was to install Mary Margaret Whipple as the new board chairman.

Milliken, who has held that job for one year, presided over the formal unanimous vote, then surrendered his post to Whipple.

Albert C. Eisenberg replaced Whipple as vice chairman.

As board chairman, Whipple will earn $12,864 a year; other board members make $11,577.

Whipple, 45, former chairman of the county School Board, lauded Milliken for registering a "perfect 10" in his year as board chairman.

In remarks she said were "as close as we come to a state of the county speech," Whipple declared that Arlington is in "excellent health and ready for the year ahead," citing the county's growing commercial tax base and a real estate tax rate that is among the lowest in the metropolitan area.

In her first action as chairman, she proposed that the board establish a bipartisan commission on Arlington's future to examine the county's long-term needs and "to assess where we want to be in the year 2000" in terms of population, county government services, schools, neighborhoods, recreation and the local economy.

Whipple said she would formally submit her proposal on the new commission at the board meeting Jan. 25.

She also urged the board to undertake "a major tree-planting project" that would enlist civic groups as well as government agencies in beautifying the county.

She called planting new trees "measures of our commitment to the next generation."

Milliken, who will remain on the board, warned that despite the rosy outlook in Arlington, 1986 would be "a year of crisis in transportation" in the region because of a threatened federal cutoff of Metrorail construction funds.

Milliken serves on the Northern Virginia Transportation Commission and is expected to become its chairman when the group convenes today.