Ted, do you have bunnies in your vicinity? They will taste almost anything that looks green and crunchy. My bunnies, however, thankfully don't like nasturtiums. I guess the spiciness is not to their taste - probably a beneficial adaptation by the plant. Isn't nature amazing.
I did have the beautiful dark red decorative sweet potato vine all over my yard as groundcover in previous years, but the bunnies definitely like it, so it only survives where it's planted up out of reach. Not great climbers, bunnies. You'd think they could jump up onto high pots to get to food, but they don't seem to ever do that.
Iguanas of various types definitely do eat plants, as well as probably insects and they are excellent climbers, so I'm hoping the weather does continue to cool off enough in winter to make them fall out of the trees here. They've been seen on the barrier islands within just a few miles of here, but not many. They're great swimmers, too.