The first ladies of the United States and the Soviet Union have completed a second good-will exchange of letters, the White House announced yesterday. According to White House spokesman Larry Speakes, Raisa Gorbachev has replied to a Nov. 25 letter that Nancy Reagan sent after the Geneva summit.

The first ladies had written to each other last fall before the summit, an exchange that led to their teas for two in Geneva while their husbands met in the summit meeting.

In her recent letter, said Speakes, Mrs. Reagan "wrote to Mrs. Gorbachev expressing her personal thank-you for the Gorbachevs' hospitality and their gifts to the Reagans. She also said she was very pleased about the results of the meeting between the president and General Secretary Gorbachev. She said she looked forward to meeting with the Gorbachevs this year in the United States."

Mrs. Gorbachev's reply, dated Dec. 21, "called attention to the 'special mood' of Geneva," Speakes continued, "and she said 'the good spirit of Geneva will live on.' She expressed best wishes for Christmas and the New Year."

Ambassador to the Soviet Union Arthur A. Hartman delivered Mrs. Reagan's letter and Mrs. Gorbachev's reply was, in turn, brought by Soviet Ambassador Anatoliy Dobrynin's wife Irina to the White House, Speakes said. Mrs. Gorbachev's letter, which was accompanied by a cover letter, "was typed but personally signed by her. An English translation was provided."