Ride 'em Cowboy! Here come the thundering hoofbeats of horseback diplomacy, which could be a brand new approach to what ails the world.

That's the way it's beginning to look from the Double-R Corral on Pennsylvania Avenue now that Queen Elizabeth has made it clear that her idea of the royal treatment is to have President Reagan join her for a canter through Windsor Great Park in June when he and the first lady are her house guests.

Reagan, who isn't expected to bring his own horse or even his own saddle, will have the distinction of being the first U.S. president since Woodrow Wilson to stay at Windsor Castle, primary home of the British royal family, built 900 years ago by William the Conqueror. It is also possible that Reagan is the first American president ever to ride with a British queen.

Flying to Europe today to tie up loose ends on the president's June 2-11 summit trip are presidential aides Mike Deaver and Bill Sittmann, with Nancy Reagan's chief of staff, Jim Rosebush. Originally a seven-day trip, the Reagans' itinerary now includes four days and five nights in Paris and a stop in West Berlin.