Well, I'm no expert on Texas caterpillars because frankly, you guys get a LOT of different kinds of stuff out there but I would lean toward a moth of some kind. Hard to tell how big they are from the photo, though. I'd say if they're not eating all your plants down to the stem or covering your house, just leave them alone. That being said, every so often we get invaded by Tussock moths here at my house and they do eat anything and they do build little cocoons all over the house, the boat, the travel trailer, etc. I just go around the house, knock them to the ground and step on them. I can't afford to use chemicals because I could possibly kill all my good caterpillars. Or if you're squeamish, you could knock them into a bucket of water (some may still manage to climb out so watch them).
Oh and like Janet said, caterpillars don't mate - they wait until they're in adult form to do that (butterfly or moth). They probably are looking for a place to build their pupa. So unless they're covering your house - and I've totally been there - I'd just leave them alone. Or maybe you could compromise and leave a few to keep the population going.
