I'm skeptical about the naginata claim. There is probably a difference in size in naginata used by men on the battlefield, and naginata known to be used by women; the latter will, on average, be smaller. But this is affected by age. Earlier naginata tended to be larger, with blades becoming shorter and lighter in later times, even when naginata were still a major battlefield weapon (they largely disappeared from the battlefield in the 16th century, as warfare went to pike (i.e., long yari) and musket). Edo Period naginata were, on average, even smaller - even the ones carried by men. It's these late naginata that we know were used by women.
Tomoe Gozen, a famous woman warrior of the 12th century, is often portrayed with a naginata. However, the written sources describe her as armed with a powerful bow and a large sword. I.e., equipped the same as a male samurai, but with a stronger bow and larger sword.
https://en.wikipedia.org/wiki/Tomoe_Gozen
Anyway, women don't seem to have difficulty wielding quite large naginata:
https://www.youtube.com/watch?v=wem9KZeFKEA