Even with how many simultaneous worldwide releases the switch gets, don't get hyped for March 22 release Past warriors games release dates:
HW Wii u
JP - Aug 14
NA - Sept 26

HW 3DS
JP - Jan 21
NA - Mar 25

Fire emblem warriors switch
JP - Sept 28
NA - Oct 20 (but I think the 3ds versions released same time? Not sure.)

With just over 2 months until release in Japan I'm sure we'll get more info and a worldwide release date soon, but until Koei/Nintendo says otherwise I wouldn't expect the game to land on western shelves until some time after March 22 unless there's a good reason to guess otherwise. 