Many of the Mormon Colonists settled in Arizona before jumping the border into Mexico. In reality there probably wasn’t much difference in pioneering a far-flung settlement in the Arizona desert to pioneering a far-flung settlement in the Sonoran or Chihuahuan desert. Both sides of the border had hostile Apache Indians and blood-thirsty banditos.
Here is a link to a Billy the Kid website which may very well place Billy the Kid in Arizona at the time the Farnsworth’s were living there.