Of the choices given, the only one I'm familiar with is Poison Oak. I'm going with it might, even probably, is Poison Oak. Around here it takes many forms, small bush, tall bush (up to 15') climbing vine (I've seen it 30' up in oak and pine trees), and creeping vine along the ground. It has various leaf forms (and color) depending on the type and age of the leaves. It's a real sneaky bugger. Almost impossible to spot after the leaves fall. In the spring it's sometimes hard to tell he young Poison Oak from young blackberries. That said, Poison Oak leaves are *generally* shiny, and the twisty tendrils look more like wild grape. Grape and Poison Oak can be hard to tell apart at times, also. I think I would treat it as Poison Oak until proved otherwise. That is, I would treat it with Round-Up. And no burning it. let it rot in place. I have been unable to find out how long the oils are active in a compost pile, but I know from experience that it's over a year. (I react rather violently, so I tend to be cautious around the stuff.) When living in the SF Bay Area I could swim in it and had no reaction. When I moved to the Foothills I gradually reacted worse and worse. to the point where once hospitalization was considered. I think the change started when I first started as a FF/PM up here, and responded to a vehicle accident where the car rolled through a large thicket of the stuff. Since I didn't react to it (I thought!), I charged right down to the car to render aid, coming out with a number of scratches from broken Poison Oak branches. I got a small amount of rash that time and it just got worse and worse with each exposure.Being a Firefighter, I was *very* concerned about smoke from burning Poison Oak, But the ambulance (and the water tender I operated when responding off-duty) generally got to park upwind of the fires, and I guess I was lucky.
Anyway, I vote for Poison Oak until proven otherwise.
After looking at the picture some more, it does look a lot like wild grape. If it forms clusters of fruit, it's grape. It's still uncertain, so I'd treat it with respect. Of course, you're in Texas, and I'm familiar with California growth, so who knows.