The cactus pictured is Cylindropuntia leptocaulis, the Desert Christmas Cholla. It is one of the most widespread of the cholla cacti. They are found in western Texas, Oklahoma, New Mexico, Arizona and northern Mexico. When taller plants are around this species will grow beneath them and use them as a trellis to support taller growth. The cactus in these photos was growing along and using the support of a barbed wire fence, and it was beneath a tree.