Historical Humans in the Southwest (a condensed version of sorts).
The Vikings came to North America and settled (temporarily, anyway) around the year 1000. They always sailed with herd animals, especially sheep.
For various reasons, the Vikings didn't stay too long.
The Navajo wandered into the present day Southwest, from the north, in the 1300s, possibly earlier. They subsisted primarily as hunters and gatherers. There is some speculation that they herded animals with them, perhaps from Asia, perhaps animals (sheep?) they found on this continent. Perhaps stock from the Vikings? Unlikely, but not impossible.
In 1493, Christopher Columbus returned to the New World on his second journey and left sheep - Churras (common working man's sheep) - on Cuba and Santa Domingo, possibly as a breeding stock for the future. (Side note: Cattle were also left on the islands - corriente or criollo cattle - the bovine equivalent of the churra).
Then, the Spanish Conquistadors began to explore the continent, - massive expeditions, taking thousands of sheep (many if not most from Cuba and Santa Domingo) with them for a steady supply of food (not that the sheep and conquistadors all traveled together at all times). Cortez, Coronado, and others pushed into the Southwest, but it's probable that Antonio de Espejo had the first direct contact with the Navajo in 1582. He didn't give them sheep to start their own herds, but the churros and the Navajo were getting closer to each other.
In 1598, Don Juan Onate had 2900-5000 sheep (probably depending upon when the sheep were counted) on his expedition into New Mexico. Settlements were started, mostly around the Rio Grande, supported by the Spanish government, from their strongholds in Mexico. Peaceful Pueblo Indians already lived in these areas. They grew cotton and weaved cloth. Were the Spaniards weaving? No one is too sure. The Pueblo Indians quickly figured out wool and begin weaving with wool and no doubt obtaining churro sheep.
The Navajo did their own thing (which included hunting and gathering and raiding and maybe stealing sheep) and the Pueblo Indians did their own thing, until the 1650s-1680s when the Pueblo Indians united and revolted and drove the Spanish back down south to Mexico. Temporarily.
In 1698 the Spanish come back with a vengeance. Many Pueblo Indians fled to the west (with some sheep), to the land of the Navajo and some assimilated with the Navajo. Definitely by this time, weaving knowledge is among the Navajo. Immediately, the Navajo seem to have checked out the Pueblo looms and nodded politely, then developed their own style of loom - the vertical loom - still used today. Loosely, 1690 is often cited as the beginning of Navajo weaving.
All throughout the 1700s, Navajo weavings are mentioned, usually in reference to their excellent quality, in Spanish records.
Sheep History
Sheep were domesticated as long ago as 9000 BC, near present day Iraq. Later, in the area of New Iberia (Spain), a common sheep was developed (or naturally selected). They did quite well in the arid, rugged terrain that was very similar to the Southwestern U.S. Small, rugged with coarse wool, these sheep were low maintenance and quite hardy. Unlike the coveted Merino sheep of royalty, these were the sheep of the working class. These churra (or common) sheep were the ones that Columbus chose (or more likely the only ones available), but regardless, they were on the way to North America in the late 1400s, becoming the first (except for the Vikings and maybe with the migrating humans) domesticated sheep on this continent.
Navajo and the Churro
Even though the Navajo had been in the Southwest for centuries before the sheep came to them, they had been waiting. Oral histories and myths had told of the coming (or the second coming - oral histories indicate that the Navajo had once had sheep, but they had all died for some mysterious reason). Once the churros came to the Navajo, neither the sheep nor the Navajo would be the same.
Spider Woman instructed the Navajo women how to weave on a loom which Spider Man told them how to make. The crosspoles were made of sky and earth cords, the warp sticks of sun rays, the heddles of rock crystals and sheet lightning. The batten was a sun halo, white shell made the comb. There were four spindlesone a stick of zigzag lightning with a whorl of coal, the second a stick of flash lightning with a whorl of turquoise, a third a stick of sheet lightning with a whorl of abalone, the fourth a rain streamer with a whorl formed of white shell.
The churros fit into the nomadic life style of the Navajo as well as fitting into the arid Southwestern landscape - it seemed meant to be. For hundreds of years, the Navajo and the churros shaped each other - today, the breed is known as the Navajo-Churro. The two are entertwined.
Interesting note: Navajo-Churros carry the polycerate gene which shows itself in 4 horns. One source refered to the Spanish churros being (northern) bred for white color and (southern) for colored fleeces - the southern carried the occasional 4 horn ram. Columbus had both on his second voyage. The Navajo thought the occasional 4 horn was special and so encouraged this through selective breeding of sorts. Interesting theory, as well as possibly the churra was bred with some of the Viking's few left over sheep. Food for thought.
US Government and the Navajo-Churro
As the United States continued to grow and expand across the continent, conflicts between the Native Americans and the government increased. The gold rush in California in the mid 1800s became the catalyst for hundreds of thousands of churro sheep to be driven from New Mexico to California. Various treaties were made and broken between the Indians and the US, until finally - starting in about 1863 (the American Civil War was going on during this time), the US Army instigated a scorched earth policy (shock and awe?) against the Navajo. Crops were burned and livestock was killed, culminating in Kit Carson driving the Navajo from their homeland (Eastern Arizona and Western New Mexico) and forcing them on The Long Walk to Bosque Redondo in 1864. (Interestingly enough, Kit Carson drove thousands of Churros from Taos to Sacaramento in 1853).
In 1868, The Navajo were allowed to return to their homeland. They were given sheep, including Churros.
Later, government Indian agents, attempted to 'improve' the breed (never mind centuries of natural selection) by introducing Rambouillets and Merinos and others. This served to either change or dilute the Navajo-Churro breed.
In the 1930s, the - citing drought conditions and over grazing issues - gov't initiated a massive livestock reduction (shooting them) program on the Navajo Reservation.
Today
Thankfully, in the 1970s and 80s, individuals began acquiring old style sheep (Navajo-Churros) from isolated pockets of the Southwest with the intent of preserving the breed and revitalizing stock. Today, the breed is listed as rare, but not endangered. The Navajo-Churro Sheep Association is responsible for registering Navajo Churro sheep and promoting and preserving this All-American breed.