Ask Mr. Smarty Plants

The USDA Plants Database lists 57 native trees (this includes subspecies and varieties) in Uvalde County, Texas.  You can perform a search and see the list yourself by choosing Advanced Search from the sidebar on the home page.  In Part A: PLANTS Core Data under 1. Distribution, scroll down through "County Distribution" and select Texas:Uvalde.  Under 2. Taxonomy check Display beside "National Common Name".  Under 3.  Ecology select Tree under "Growth Habit" and select Native to PLANTS Floristic Area under "Native Status".

You didn't say what sort of tree you were looking for, but here are a few recommendations from that list.  You can follow the link and read more about each species in our Native Plant Database:

Acer grandidentatum (Bigtooth maple) grows to about 15 feet and has beautiful red fall foliage.

Cercis canadensis (Eastern redbud) can reach 30 feet and has pink spring blossoms.

Chilopsis linearis (Desert willow) can grow to 40 feet with large, showy blossoms that follow summer rains.

Fraxinus albicans (Texas ash) grows to 30-45 feet with a densely branched canopy and striking fall colors.

Juglans microcarpa (Little walnut) usually grows to only about 20 feet and has fruit enjoyed by squirrels.

Morus microphylla (Texas mulberry) small (12 to 16 feet) tree or shrub with edible berries.

Platanus occidentalis (American sycamore) large (75-100 feet) tree with a massive trunk and large maple-shaped leaves.

Prunus serotina (Black cherry) large (25 to 110 feet) tree with yellow fall foliage and fruits that can be made into jelly or wine.

Ptelea trifoliata (Wafer ash) small (10 to 15 feet) tree or shrub with yellow fall foliage.

Quercus fusiformis (Escarpment live oak) reaches 20 to 40 feet and is evergreen.

Sophora secundiflora (Texas mountain laurel) usually multi-trunked and grows to 10-20 feet, evergreen with beautiful purple spring blossoms.

Ungnadia speciosa (Mexican buckeye) small (up to 30 feet) tree with pink spring blossoms.