There probably aren't many for political reasons but anyone got recommendations where the princess of a Western nomad-ish tribe is featured prominently or even a lead or romantic partner to a lead? And she contrasts with the other women in the show because she goes out horse riding, hunting, etc...

I'll also take any suggestions for noble women who grew up free of the constraints of typical women. Not particularly interested in birth secrets involving these characters but since I imagine selection will be limited go ahead and suggest those ones as well.

The Legend of the Condor Heroes has a Mongolian princess.  She's a major character early in the drama, but later becomes a minor character.

I've only seen the 1983 version, but they're all based on the same novel, so I assume she's probably in all of them.

I think that recent drama Legend of Xiao Chuo with Tiffany Tang 

It's a kdrama, but Empress Ki is set in Yuan, so there are a number of Mongol women who are major characters. There is also a part where women participate in a hunt. FL is Korean, but she grew up disguised as a man, so she knows how to fight, ride, and is an excellent archer.

Good Bye, My Princess as I remember FL is mongolian tribe princess and tribe life is beautifully shown. 

wasn't it mongolian tribe?