War Paint (1953)

Lieut. Billings and his army patrol are ordered to deliver a new peace treaty to the Indian Commissioner, who is missing. They have nine days to get the treaty to Chief Gray Cloud or there will be war. Chief's son Taslik offers to guide them. But as their water runs low and conflicts escalate, they can't help wondering why Taslik is wearing war paint.

IMDb: https://www.imdb.com/title/tt0046533