Most women fought in wars because they decided to, not because someone let them. The modern armed services can be seen as a concatenation of one law and reg after another to keep women out of combat, where they would otherwise go, until the 21st C unwound this.
“The first history”, Herodotus’, includes the record of woman warriors. There is Tomyris of the Massagetae, a horse tribe of the Sea of Grass, who defeated and killed Cyrus the Great (Kurush), and Artemisia I of Halikarnassos, queen regnant and satrap for Xerxes, who was so effectual the Hellenes had a huge bounty on her head even before Salamis.
You can find a lot of female warleaders, from Æthelflæd of Mercia, daughter of Alfred the Great, to Countess Matilda of Tuscany. (You can find them in, say, Tim Newark’s Woman Warlords) But instead, let’s talk about cultures where women “were allowed combat roles” – cultures where woman warriors were not considered odd. Then we’ll discuss cultures that couldn’t stop the women.
Woman warriors were completely normal among the Sarmatians/Scythians/Sakas who left their kurgan burials across the steppes. A large number of skeletons that could be sexed as female by the pelvis were buried with weapons. Normally weapon burials are assumed to be male. In modern days, a number of “assumed male” burials have been reconsidered, notably the Golden Prince. ( Dr. Jeannine Davis-Kimball, “Chieftain or Warrior Priestess?” in Archaeology, Sep/Oct 1997) The female headdress should have been a tip-off, but weapons meant it just couldn’t be a girl! So in this culture one in five provably female burials were warriors, including the one buried with a young male across her feet for a good time in the afterlife. (Sulimirski, The Sarmatians) That these people lived where the classical Greeks said the Amazons did seems a bit beyond coincidence, no matter how the Greeks warped their stories later.
Frankish women sometimes led their own warband (scara). A notable one was Perhalta, modernized as Bertha of the Big Foot, mother of Charlemagne.