The unanswered question around the White House and the State Department this week is whether Mikhail Gorbachev will bring his wife Raisa to Washington next month.

Gorbachev's letter to President Reagan proposing a summit date and an agenda apparently never got into the incidentals of the visit -- if one can call Mrs. Gorbachev incidental.

Unofficial observers of the Soviet scene say that it's not surprising the Soviet first lady hasn't been mentioned yet, since the Soviets don't place the same emphasis on the participation by their leader's wife in official life that Americans place on theirs. Before Mrs. Gorbachev, the wives of Soviet leaders were seldom seen in public, and almost never heard from.

"A wife taking part is totally new to them," says Betty Bumpers, president of Peace Links, a grass-roots effort that sent an 18-member delegation to the Soviet Union last month at the invitation of the Soviet Women's Committee.

Contrary to their earlier expectations, the Peace Linkers never got to meet with Mrs. Gorbachev. Nor were they able to find out whether she had indeed been seriously ill, as was reported in a story that also suggested it as the reason for Gorbachev's two-month hiatus from public appearances this fall.

Bumpers, wife of Arkansas senator Dale Bumpers, said the women's committee members are careful to point out that Raisa Gorbachev's participation in their group is as a representative from her Soviet republic and not as the wife of the general secretary.

"They are very proud of her," said Bumpers. "I never heard any negative criticism of her."

In fact, Bumpers said that since she had been in Moscow last winter, "I don't know whether it's Raisa's influence or the fact that there is a lot more exposure because Americans are everywhere, but the Soviet women are dressing better, their haircuts are better, there is definitely a difference in how they look."

Bumpers' report provides a somewhat softer view of how Raisa Gorbachev is perceived at home than that brought back by another recent visitor, who says the attention paid Mrs. Gorbachev is contributing to suspicions that "a cult of personality" is growing up around the Gorbachevs.

"They believe that women should be seen but not heard, that Raisa is too visible, that she has no significant influence and that her image is the product of the Western media," said this source, a longtime observer of the Soviet diplomatic scene here who asked to remain anonymous.

"In other words," the source continued, "that we've built her into something she ain't."

President Reagan continues to hope that he'll someday be able to show off the United States to Gorbachev, particularly the Reagans' California ranch.

"I would still like to do that," Reagan told reporters who asked if he was disappointed that Gorbachev's December visit will be too brief to allow a cross-country tour.

At a White House press briefing Friday, with Secretary of State George Shultz and Soviet Foreign Minister Eduard Shevardnadze standing beside him, Reagan recalled that in Geneva when he and the Soviet leader discussed getting together again for summit meetings in the United States and the Soviet Union, "he suggested that there might be things in the Soviet Union that he would like to show me."

"Like a gulag," an unidentified voice noted wryly.

Israeli President Chaim Herzog and his official party will be served a kosher dinner at the White House next week. For everybody else on the Reagans' state dinner guest list, it will be pick-and-choose.

"As people call in, they are being asked if they prefer a kosher meal," Elaine Crispen, Nancy Reagan's press secretary, said yesterday of the Nov. 10 dinner. "Those who don't will get a regular meal."

Unlike Jimmy Carter's dinner for Menachem Begin, when the entire White House kitchen was "koshered" by a blowtorch-bearing mashgiah (the rabbi who supervises a kosher kitchen), the kosher part of Ronald Reagan's dinner for Herzog will be catered.

The as yet unidentified caterer will prepare the food elsewhere and then deliver it to the White House. The nonkosher meal, using the same ingredients, will be prepared by White House chefs.

Gretchen Poston, Carter's social secretary, said a mashgiah brought in a blowtorch to clean the White House ovens and silver for the Begin dinner, but that kosher dinner plates were rented from an outside supplier.

The White House went kosher another time, when Carter hosted a dinner celebrating the signing of the Israeli-Egyptian peace accords by Begin and Egyptian President Anwar Sadat. That time, however, a caterer set up a separate kosher kitchen adjoining the tent in which the dinner was held. To keep the peace accords completely peaceful, the food for Carter's Arab and other guests was cooked in the White House kitchen.

Nancy Reagan will be answering her voluminous mail in the aftermath of her mother Edith Davis' death but otherwise will take it easy for the rest of the week, according to her spokeswoman Elaine Crispen.

Tonight, for instance, Mrs. Reagan will stay upstairs in the family quarters while the president is downstairs in the State Rooms at a reception for the Friends of Art and Preservation in Embassies.

Mrs. Reagan may be out of sight, but not out of touch, however. Two days before her Oct. 17 surgery for breast cancer, the first lady videotaped several messages about drug abuse, some of which will be heard at regional meetings of the White House Conference for a Drug Free America, which gets underway this week and continues into mid-December.

Attorney General Edwin Meese is scheduled to speak tonight at the opener in Omaha, where others on the program will include Olympic gold medalist Mark Spitz and former Chicago Bears running back Gale Sayers. Two other messages taped were for last week's Washington Charity Awards Dinner, which is expected to raise $200,000 for the Nancy Reagan Drug Abuse Fund, and a January PBS-TV special produced by the Scott Newman Foundation, named for actor Paul Newman's son, who died of a drug overdose in 1978.