Washington's National Gallery of Art rings in the new year with a continuation of its Saturday morning family program "Discover the Gallery." This weekend, you can see a slide show about English country houses, then learn about the Treasure Houses of Britain with a self- guided mystery hunt that involves finding items in the exhibition. Reservations are required.

The following events are free unless otherwise noted.

NATIONAL ZOO -- Open daily; gates open from 8 to 6; animal buildings, 9 to 4:30. Elephant training demonstrations, 2; Sea lion training demonstrations, 11:30. The Panda House is again open; feedings at 11 and 3. 3001 Connecticut Ave. NW (Rock Creek Park), on the Metro Red Line. Family learning centers Zoolab and Birdlab open Friday through Sunday, noon to 3; Herplab open Wednesday through Sunday, noon to 3. 673-4717.

OXON HILL FARM -- Open daily, 8:30 to 5, Oxon Hill Road (take Beltway exit 3A, turn right on Oxon Hill Road). Saturday-Sunday, 3 to 4:30, milk a cow, collect eggs and feed the animals; meet at barnyard. 839-1177.

NATIONAL AQUARIUM -- Open daily, 9 to 5, Department of Commerce, 14th and Constitution Avenue NW. The sharks are fed Monday, Wednesday and Saturday at 2; weekday features are a touch-tank, mini- theater and a thousand types of marine life. School groups should schedule in advance. Adults $1; children 50 cents. 377-2825.

CEDAR HILL -- Open daily, 9 to 4, 1411 W St. SE, Anacostia. Cedar Hill, Frederick Douglass' home, recalls his work with films, interpretive exhibits and a house tour. 426- 5961 or 426-5962 or 426-5963.

USS BARRY -- Open daily, 10 to 5, Washington Navy Yard, Ninth and M streets SE. The Navy destroyer's weather deck is open for public viewing and self-guided tours. 433-3377.

CHILDREN'S MUSEUM -- Monday through Saturday, 10 to 4, Sunday 1 to 4, Rose Hill Children's Museum, Frederick, Md. Take U.S. 15 north to Exit 8 to Motter Avenue; follow Motter to left onto 14th Street and left onto North Market Street, follow signs to Rose Hill. Costumed tour guides conduct tours of the 1790 mansion. Hands-on exhibits include a loom, antique toys and spinning wheel. Adults $1; under 17, free. 301/694- 1646.

CAPITAL CHILDREN'S MUSEUM -- Daily, 10 to 5, 800 Third St. NE. Friday, 10:15; Saturday and Sunday, 1 and 2:30, "Aladdin." The Puppet Company performs the story of a lamp brought to life. Museum admission is $2; "Aladdin," an additional $2.50. 543-8600.

DOLL'S HOUSE AND TOY MUSEUM -- Tuesday through Saturday, 10 to 5; Sunday, noon to 5, 5236 44th St. NW. A collection of antique dollhouses, dolls, toys, games and an exhibit of antique cat games and toys. Adults $2; under 14, $1; group rates available. 244- 0024.

DISCOVERY THEATER -- Tuesday-Friday, 10 and 11:30 a.m.; Saturday, 1 and 3, Discovery Theater, Arts and Industries Building, 900 Jefferson Dr. SW. Classic Stories, Enduring Tales: "Peter and the Wolf," with shadow puppets. Recommended for grades K-4. Adults $3; 12 and under, $2.50; group rates available. For more information and reservations, call 357-1500.

CLOISTERS CHILDREN'S MUSEUM -- Wednesday through Friday, 10 to 4:30; Saturday-Sunday, 12 to 4, 10440 Falls Rd., Brooklandville, Md. (just outside Baltimore). Saturday-Sunday, museum hours, use tissue paper to make a stained glass window; $1 materials fee for workshop. Museum admission: $2 donation requested from adults; group tours available. 301/823-2551.

RAILROAD STATION MUSEUM -- Wednesday through Saturday, 11 to 4; Sunday, noon to 5, Main Street and Maryland Avenue, Ellicott City. The renovated station has a diorama of the trip of Tom Thumb (an early 19th-century train) from Baltimore to Ellicott City. There are also sight and sound shows, model train exhibits and tours of the museum. Adults $1.25; under 13, 75 cents. 301/461-1944.

CHILDREN'S RADIO THEATER -- Saturday, 8 a.m., WPFW 89.3 FM. "Two Brothers and the Panther Suit," a story about dangerous dealings with wizards, lake monsters and sorcerers. Listeners can participate in a call-in following each program by calling 783-3104.

SATURDAY MORNING AT THE NATIONAL -- Saturday, 9:30 and 11, Helen Hayes Gallery, National Theater. Checkers the Clown entertains with magic, mime, song and storytelling. Reservations recommended. Call 783-3372, 24 hours a day.

DISCOVER THE GALLERY -- Saturday, 10 to 11:30, National Gallery of Art, Fourth and Constitution Avenue NW, "The Treasure Houses of Britain." A program for families with children six to 12. See a slide show on country houses, followed by a self-guided mystery hunt through the exhibit. Free, but advance registration required. 842-6249.

NATURE HIKE -- Saturday, 10 to 11, Clearwater Nature Center, 11000 Thrift Rd., Clinton, Mdds four to seven can explore the outdoors; reservations necessary. 297- 4575.

PRE-SCHOOL STORYTIME -- Saturday, 10:30, Children's Room, Mt. Pleasant Branch, D.C. Public Library, 16th and Lamont streets NW. Slide shows and storytelling for pre- schoolers. 727-1361.

OLD POST OFFICE -- Saturday, noon to 1, The Pavilion, 1100 Pennsylvania Ave. NW. The Performance Company, a local kids' group, sings and dances to popular show tunes in this children's cabaret. 289-4224.

TROLLEY MUSEUM -- Saturday and Sunday, noon to 5, Northwest Branch Regional Park, Bonifant Road between Layhill Road and New Hampshire Avenue, north of Wheaton. Trolley rides: $1 adults; under 18, 75 cents; under two, free. 384-9797.

MUSEUM OF AFRICAN ART -- Saturday, 12:30, 318 A St. NE, "Storytime at the Museum in the Oral Tradition," African lore from experienced storytellers; 1 to 3, "Mbira: The Thumb Piano," children eight and up can make a small musical instrument and learn how to play it; pre-registration required. 287- 3490, ext. 32.

CHILDREN'S PLANETARIUM -- Saturday and Sunday, 1 and 4, Rock Creek Nature Center, 5200 Glover Rd. NW. First show for children four to seven (must be accompanied by an adult); second show, for ages seven and up. No latecomers are admitted. 426-6829.

NATURE FILMS -- Saturday-Sunday, 2, Gulf Branch Nature Center, 3608 N. Military Rd., Arlington. "After the Whale," a half-hour film about the earth's largest mammal. 558-2340.

MAGIC SHOW -- Saturday, 2, Capital Plaza Shopping Center, 6200 Annapolis Rd., Hyattsville. Hal Diamond performs magic tricks. 445-4500.