Billy Carter is back home in Plains, Ga., for the Christmas holidays, taking a break from his lengthy chemotherapy treatments, and says he feels confident he will "lick" the inoperable pancreatic cancer that was discovered in September. The 50-year-old brother of former president Jimmy Carter, to whom his drinking became such a political embarrassment, said he hopes to have a clean bill of health in a few months.

He said, however, that if he doesn't defeat the disease that killed his father and his sister, "I hope I will have lived a useful life and had something to offer other people." He said his brother, who lives two doors away in Plains, visits him twice a day and recently brought him a Louis L'Amour novel to read. Two days after Christmas, Billy Carter will return to Emory University Hospital in Atlanta to resume treatment. Carter and his wife Sybil have six children. Out and About

Television journalist Roger Mudd remembers Union Station as a sea of military uniforms in 1944, when he was part of the vast buildup of servicemen going off to war. Sen. Edward Kennedy has a more recent memory of a Boston snowstorm about six years ago when he took the train back to Washington with a group of Marines traveling to Quantico, listening to their views on military life and defense spending. Such Union Station nostalgia will come up more often in conversations around town as the venerable Roman palace, to be reopened next year, becomes a Capitol Hill presence with shops, cafe's and theaters.

In October, The New Republic magazine ran a cover cartoon of Mayor Marion Barry, portraying him as a Caesar wearing a laurel wreath and holding a rolled-up $100 bill in his hand while an overripe, underdressed maiden pops a grape into his mouth. In the most recent issue of the magazine two letters of protest were published, signed by the Rev. Canon Kwasi A. Thornell of the Washington Cathedral and Dalton D. Downs, rector of St. Timothy's Episcopal Church. The odd thing about the two letters is that they were identical except for the last four words.

Wall Street Journal Supreme Court reporter Steve Wermiel has been quietly working for nearly a year on a biography of Justice William Brennan for William Morrow Co. The 81-year-old Brennan has agreed to cooperate with Wermiel with the understanding that the book will not be published until after his death ...

Washington attorney Jack Olender, who last year created the annual Olender Peacemaker Award, last night presented this year's honor to Soviet leader Mikhail Gorbachev and President Reagan. The award was accepted by Soviet Ambassador Yuri Dubinin and Thomas W. Simons Jr., deputy assistant secretary of state, at the J.W. Marriott. In connection with the award, Olender donated $25,000 to the United Black Fund. Last year's first honoree was Dr. Robert Gale, the bone marrow specialist who treated the Chernobyl nuclear disaster victims ...

Mary Barton, who danced the lead role of Clara in the Joffrey Ballet's new version of "The Nutcracker" at the Kennedy Center Opera House Wednesday night, was making her Washington debut in the same theater where she was once an usher. The daughter of Charles and Mary Lee Barton of Arlington, the 27-year-old Barton grew up there and studied under Mary Day at the Washington School for Ballet ...

It looks as if Madonna has decided to give Sean Penn a second chance. According to documents filed Wednesday in a Santa Monica, Calif., courtroom, the pop diva -- who sought a divorce from the ill-mannered actor just two weeks ago -- has requested and was granted dismissal of her divorce petition. No reason was given for the "Who's That Girl?" girl's change of heart ...