In many American homes these days the television set has replaced the old-fashioned hearth as the center of family holiday activities. TV programmers have therefore scheduled a wide array of family-oriented specials for Christmas week. Here are some of the most noteworthy (please check local listings): FRIDAY Babes in Toyland (NBC, 8-11 p.m.): Remake of movie version of Victor Herbert operetta [previewed at right]. SATURDAY

Christmas Snow (NBC, 8-9 p.m.): Sid Caesar and Katherine Helmond in a story about a widow and her two adopted children as they face holiday eviction.

Christmas in Washington (NBC, 10-11 p.m.): John Forsythe is host and Mac Davis a guest in the fifth annual telecast of the traditional special entertaining Washington notables, including President and Mrs. Reagan. SUNDAY

Bob Hope's Bagful of Christmas Cheer (NBC, 9-10 p.m.): Comedian Hope hosts program of holiday sketches and songs by Crystal Gayle, the youngest Osmonds, Brooke Shields, and others, as well as Pasadena's Rose Queen and the AP All-American football team.

Amy Grant: Headin' Home for the Holidays (NBC, 10-11 p.m.): Gospel singer Grant is joined by Art Garfunkel, Jimmy Webb, and others performing traditional Christmas songs in the Big Sky country of Montana.

A Christmas Gift (CBS, 9-11 p.m.): John Denver portrays a big-city architect who fights rural redevelopment - in the Rockies yet again. MONDAY

Barbara Mandrell's Christmas: A Family Reunion (CBS, 10-11 p.m.): Barbara and her sisters sing, play instruments, perform magic, and kid around together, all in the holiday spirit.

A Christmas at Pops (PBS, 8-9 p.m.): The Vienna Boys Choir and the Tanglewood Festival Chorus join conductor John Williams and the Boston Pops for a holiday celebration at Boston's Symphony Hall.

Christmas Eve (NBC, 9-11 p.m.): Loretta Young, in her first movie role in 23 years, plays a wealthy widow determined to leave a legacy of Christmas-time good deeds. With Trevor Howard and Arthur Hill. TUESDAY

A Christmas Carol (CBS, 9-11 p.m.): Repeat of George C. Scott's classic portrayal of Scrooge, filmed in England in 1984.

A Christmas Carol (Arts & Entertainment/cable, 9-11 p.m.): San Francisco's American Conservatory Theater production of the same Dickens classic. WEDNESDAY

A Festival of Nine Lessons and Carols (PBS, 8-9 p.m.): The Christmas story in Bible readings and music from the chapel of King's College in Cambridge, England.

Amahl and the Night Visitors (CBN/cable, 8-9 p.m.): Repeat of Gian Carlo Menotti's opera about three kings who visit the baby Jesus.

Christmas at Radio City (HBO/pay cable, 8-9 p.m.): Joel Gray hosts holiday on-stage party.

Christmas Eve on Sesame Street (PBS, 9-10 p.m., check local listings): Big Bird hosts a Muppet party, complete with a Santa of sorts.

The Night They Saved Christmas (ABC, 9-11 p.m.): Repeat of whimsical musical in which Santa (Art Carney) and his toy factory at the North Pole are endangered by oil prospectors.

Robert Shaw's Christmas Festival (PBS, 9-10:30 p.m.): Atlanta Symphony Orchestra director Shaw conducts choir and orchestra in hymns, carols, and Christmas instrumental selections from around the world.

Trumpet of Conscience (WTBS/cable, 10:05-11 p.m.): Inspired by Dr. Martin Luther King Jr.'s 1967 Christmas Eve sermon, this prize-winning documentary explores his philosophy of social change through nonviolence (Repeat). THURSDAY

The Walt Disney World Very Merry Christmas Parade (ABC, 10-11 a.m.): Live from Orlando, Fla., with Snow White as grand marshal. John Lunden and Ben Vereen host the procession.

A Christmas Memory (PBS, 8-9 p.m.): Repeat of autobiographical Christmas reminscence, written and narrated by Truman Capote and starring Geraldine Page.

A Gift of Love: A Christmas Story (CBS, 9-11 p.m.): Repeat of Earl Hamner's poignant tale of a New England holiday with Angela Lansbury, Lee Remick, and Polly Holliday.

Love Boat Christmas Special (ABC, 8-10 p.m.): The same old things keep happening on this Christmas cruise. Well, it's a change of pace from other predictable Christmas fare.

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