...there are plenty of live oak, elm, juniper, hackberry and mesquite trees
Both sides of Hardberger Park (on NW Military and Blanco) have plenty of live oak, juniper, hackberry, mesquite, and cedar elms. However, the Texas red oaks (Quercus buckleyi) are confined to the Salado Creek area (on the Blanco side). This is due primarily to soil type. Texas red oaks tend to grow mainly in the "limestone outcrops and slopes or in stream bottoms..." (Flora of North Central Texas by Shinner and Mahler). The only real limestone outcrop we have at the park just so happens to be over along the creek. They also like areas that receive more moisture and are more mesic. These are areas that are well drained and typically do not have deep soils. All the other species listed tend to grow in a wide variety of soils and ranges and can typically handle a bit less mesic conditions.