Moscow — The Kremlin daily Pravda gave its readers a peek into Soviet leader Yuri Andropov's mailbag. The letters were sent to him by Americans. ''I don't think you will listen to me, because I'm just a little American boy ,'' wrote teen-ager Andrew Broman from Lincoln, Neb. ''But I've heard a lot about you and I think you will be a good leader of the USSR.''
Pravda said the letters showed that even if those in power in the United States were aggressive, the American people still had common sense and a healthy practical approach. Most of the letters expressed support for the idea of a mutual freeze on nuclear weapons and criticized President Reagan. ''I want you to know that in our country there are people just like you,'' Mr. Andropov was told by Deborah Merritt of West Brattleboro, Vt. And Walter Kaiser of New Port Richey, Fla., said, ''Let us show the whole world that our two great countries can live in peace.''
Admittedly, the Communist Party daily said, some Americans were ill-informed. ''Why do you want to conquer the whole world or at least our country?'' asked Samantha Smith of Manchester, Maine. Pravda said Samantha could be forgiven because she was only 10 years old.
Pravda published an earlier selection of letters to Mr. Andropov in mid-February. The purpose of this latest round appeared to be to keep alive the idea of an Andropov-Reagan summit, which several letters suggested. Some analysts believe Mr. Andropov would like to hold a summit with President Reagan, but may face domestic opposition to the idea.