I believe they are seed pods. Are they full of fluffy white seeds?
Fluffy white seed pods on a mesquite? Seed pods on a mesquite are called "beans" and they look nothing like the photos luke posted. Does milkweed grow up a mesquite as a vine?
p.s.-Just did some research and redchevy is correct. It's a form of milkweed that is a climbing vine called "honeyvine" or "climbing milkweed."
Thanks Luke and redchevy. I just learned something new! Sorry I doubted you rc.