The 26-year-old Neal had 27 goals, 34 assists and a plus-15 rating last season in 59 regular-season games for Pittsburgh, and two goals and two assists in four playoff games. The six-year veteran, who has $15 million left on a six-year, $30 million deal that runs through 2017-18, will try to help a Predators offense (under new coach Peter Laviolette) that ranked 19th in the league with 2.6 goals per game.
Neal, who scored a career-high 40 goals in 2011-12, was suspended five games last season for kneeing Brad Marchand in the head.
Hornqvist, 27, is also a six-year veteran (all six in Nashville) and last season he scored 22 goals with 31 assists, while Spaling, 25, had 13 goals and 19 assists last season.
Hornqvist signed a five-year deal with the Predators last summer for $21.25 million.