Father and I Were Ranchers, originally published in 1950, is the first book in the Little Britches series.
From the 2001 audio book:
In 1906 eight-year-old Ralph Moody moves with his family from New Hampshire to a Colorado ranch for his father's health. Ralph's family experiences the pleasures and perils of ranching; attending auctions and roundups, battling with neighbors over water rights, fighting tornadoes, and scratching a living from the wild prairie sod.
Ralph meets Hi Beckman, the best ranch foreman and cowboy in all Colorado. Hi teaches Ralph all the tricks of the trade making "Little Britches" into a first-rate cowhand and rodeo rider. Ralph's friends, Hi, Two Dog, and the blue-roan cowhorse Sky High, give Little Britches all the learning and excitement a boy can dream of. He'll need it as the adventures Ralph faces will have to equip him to take his ailing father's place when the time comes....
Man of the Family