Marlo Thomas plays a fiercely independent Chinese would-be mail-order bride who mistakenly ends up with Hoss (who ordered Chinese fireworks, the joke being that is what he got).
Thomas' character anticipates the woman's movement of the mid-60s and 1970s (this is 1964) with her fight for woman's rights, organizing the cowboys to fight for better conditions, etc. However, as this is a comedy episode, it is played for laughs and the attitudes come across as more condescending and patronizing if not misogynistic.
Finally, Marlo Thomas being passed as Chinese is only embarrassing in retrospect. A single throw-away blink-and-you'll-miss-it line half-way through the episode about the character's father being a Persian (not European as another commentator noted) carpet merchant is meant to justify Thomas's obviously not Asian appearance appearance (Thomas is of Lebanese/Italian heritage). It is literally a throw-away line that seems to have been added as an after-thought and nothing else about this is mentioned nor does it become even a minor plot point. There is no effort beyond that one throw-away line to establish the character as being of mixed-race and the result is that they seem to be trying to make her pass as Chinese.
In the end, Thomas' character retires from activism for marriage. The broad comedy and slapstick might make it entertaining, but the whole tone seems more to be mocking of woman's rights than exploring woman's rights in the context of the Wild West.