The tic-tac-toe game branded on the cow could not occur in a real game - there are 4 Os and 5 Xs with "O" winning; X would not play their fifth turn once O wins the game.
The colorful background would indicate the ranch was located 'way out West, ' a popular theme in media at the time. Among the desert plants seen are the stately Saguaro and the beaver tail cactus, and what appears to be a Joshua tree (not a tree at all, but a member of the lily family).