Cowboys were not only Native Americans and Mexican Americans.
Originally, a cowboy was an animal herder that took care of cattle in many ranches in the United States. They did other activities in the ranches but in the 19th century became more famous when some of these cowboys participated in Rodeos. Cowboys had a unique style of clothing, a tough-man attitude to cattle-driving, and an adventurous mind.
The New Deal was all about social program and after FDR the Government was more involved with the public and the economy with government programs like social security etc