Were there Indian cowboys or gunmen in the Southwest?
Yes, especially among the Apache. Their lands at San Carlos and White Mountain were good cattle country. After the Apache were located on reservations from the 1870s on, they engaged in the livestock business. The Navajo have been in the sheep business since the Spanish brought the sheep into New Mexico in the early 1600s. Their reservation is better suited for sheep than cattle.
Rodeo has become a popular sport for both the Apache and the Navajo, and they’ve turned out some pretty good ropers and riders.
As far as gunmen, the Southwest Indians didn’t really produce characters such as Ned Christie or Cherokee Bill or Rufus Buck. But the Apache Kid sure gave lawmen a run for their money.