D.C. Council Chairman-Elect John A. Wilson (D) has appointed former corporation counsel Fred Cooke to head a new committee to advise him on how to reorganize the council and strengthen its role in city government.

Wilson described the move as an effort to implement his campaign promise of reestablishing the council as a coequal branch of government, after years of what he considers its subservience to Mayor Marion Barry.

Other members of the group include former council member Polly Shackleton, Ward 7 civic leader Benjamin Thomas, lawyer Max Berry, former corporation counsel John Risher, Metropolitan Area AFL-CIO chief Joslyn N. Williams and Pedro Alfonso, president of the D.C. Chamber of Commerce.

The move comes as maneuvering has begun at the District Building over who will get prized committee assignments when the new council is installed in January. According to council traditions and rules, committee chairmen have unusual power to control legislation in the areas under their purview.

With two powerful committee chairmen leaving -- Government Operations chief Betty Ann Kane (D-At Large) and Public Works head Nadine P. Winter (D-Ward 6) -- the stage is set for a substantial reshuffling of the deck, with several council members ready to assume greater responsibility.

Wilson so far has been officially mum on his plans for reorganizing the council, although speculation is rampant.

One school of thought among council insiders is that Wilson would like to break up the Housing and Economic Development Committee, currently headed by Charlene Drew Jarvis (D-Ward 4). Jarvis is not popular among her colleagues, but she is a bruising political infighter who defeated the current chairman, David A. Clarke (D), when he tried to break up the committee several years ago.

Council sources say that Frank Smith Jr. (D-Ward 1), now chairman of Public Services, has expressed interest in being chairman of a new committee on housing.

Informed speculation also has it that William Lightfoot (I-At Large) is likely to take over Government Operations, with Harry Thomas Sr. (D-Ward 5) taking over Public Works for the outgoing Winter.

Meanwhile, Jim Nathanson (D-Ward 3) is said to be in line to take over a new committee with authority over zoning and land use issues. Those issues are now in the jurisdiction of the Committee of the Whole, headed by the council chairman, but Wilson seems ready to break that up as well.

Under his plan, the Finance and Revenue Committee, of which he is now chairman, would be folded into the Committee of the Whole, which already has jurisdiction over the budget. As a result, Wilson would be in charge of an extremely powerful committee with wide-ranging authority over budget, finance and tax matters.

No wonder wags at the District Building already are calling Wilson "Mr. Mayor." Weekend Wedding

The political wedding of the fall is set for Saturday with the nuptials of City Administrator Carol B. Thompson and Norfolk contractor Curtis Cole. Virtually the entire D.C. political establishment has been invited, including Mayor Marion Barry, members of the D.C. Council and Cabinet officials, sources say. The wedding is at Asbury United Methodist Church, followed by a reception at the Grand Hyatt Hotel.

Thompson has not disclosed her career plans, though one rumor sweeping the city is that she is being considered for the newly vacant job of general manager of Metro. Scramble for Ward 2 Seat

The race to succeed John A. Wilson as Ward 2 member of the D.C. Council is already getting crowded, though the special election to fill that seat is still nearly six months away.

Dupont Circle Advisory Neighborhood Commission Chairman Jack Evan will formally file his candidacy next week. Former Barry administration aide Jim Zais has already quit the government to prepare his candidacy, and housing activist Clarene Martin recently filed to switch to the Democratic Party and is gearing up to run.

At least three other candidates also are getting set to run: Georgetown architect Bill Cochran, Southwest D.C. activist Willie Lloyd Reeves and Shaw resident Cornbread Givens.

Also, the ward's school board representative, R. David Hall, has not ruled himself out of the race, although he is said to be leaning toward an effort to gain the presidency of the school board. Radio Show Rescheduled

Political junkies, insomniacs and fans of political pundit Mark Plotkin might like to know that the D.C. political hour, a weekly hour-long discussion of D.C. politics and government, has moved to a new time: the family hour at 8 p.m. Fridays, on WAMU-FM (88.5).

What began as an experiment scarcely a year ago is now apparently a Washington institution. "Friday night has a whole new dimension," Plotkin shills. "Don't leave home without it."