Ilex vomitoria (yaupon), while a very sturdy native plant, is sometimes considered a "nuisance" plant on properties; however, it is a versatile plant that tolerates drought and poor drainage, This USDA Plant Profile does not show it growing in Concho County, northwest of Austin, but it obviously does, if you have it in your pasture.
From a previous Mr. Smarty Plants answer:
"According to Jill Nokes in How to Grow Native Plants of Texas and the Southwest:
"Most holly species are frequently and successfully transplanted from the wild or from field-grown nursery operations in the winter...."
Ilex vomitoria (yaupon), a member of the Family Aquifoliaceae (Holly Family), should readily transplant. The time to do this is now, mid-winter. It is very important, of course, to get as much of the root ball as possible when you dig up your trees. Here are some other tips in Transplanting Trees and Shrubs, from the About.com: Landscaping, and How to Transplant a Young Tree from wikiHow."
Note that this says they should be transplanted in mid-winter, especially in Texas. While this plant is often referred to as a "coastal" plant, or one able to live in swamps, we feel sure it could do well on the Edwards Plateau, where you are located. Just don't try to transplant it in the heat of the summer.
From our Native Plant Image Gallery: