You're in Dallas, right? Looks like Yaupon holly to me...it grows all over central Texas. It makes excellent arrow shafts and was a favorite of NA's. Peel the bark off right away (the bark is really tough to get off if you let it dry with the bark on) and seal the ends with wood glue (or whatever) and dry them in a warm place. They don't check much (if any) and they dry in as little as two weeks. The wood is very white, light weight, and sands easily. They are difficult to straighten, so cut only the straightest ones you can find. It is very similar to privet.....but lighter in weight.
Here's a pic of Yaupon holly:
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