Which country most influence the development and legacy of the traditional american cowboy

Cowboys originated in Mexico.

When the spanish conquerors arrived, they started stablishing ranchs and farms, and the role of the vaquero (from the spanish word vaca) was coined to  name the men who took care of the livestock, and who were also good with certain skills like herding, roping and riding.

As the ranching practices were spread, so did the culture of the cowboy, including their clothing style and their skills.

The first cowboys had different backgrounds like Mexican, Native American and African American, among others.

The country that most influenced the development and legacy of the traditional American cowboy was Mexico. When the Spanish arrived and settled in Mexico in the 16th century they operated rural estates where they raised cattle assisted by horses that had been brought from Spain. Native Indians were trained to ride the horses and herd and handle the cattle. They developed great skills at controlling the animals while being mounted, and they began to be known as vaqueros - Spanish for cowboys. By the 17th century, these estates or ranches existed in areas such as Texas, Arizona and New Mexico, as well as in Argentina - all of them part of the Spanish empire. With the expansion of the livestock industry in other parts of the Western United States (California, Idaho, Nevada) it eventually turned into an American profession in its own right, with cowboys ranching and transporting cattle to the main railroad depots for consumption all over the country.