Since we are gardeners and not entomologists, we went to the Internet to try to find an answer to your question. This article from Colorado State University Extension on Grasshopper Control in Gardens and Small Acreage contains this paragraph:
"Adult grasshoppers may live for months, interspersing feeding with mating and egg laying. Species that winter in the egg stage die out in late summer and early fall. A few species, perhaps most conspicuously the speckledwinged grasshopper, spend winter as a nymph, remain active during warm periods, and may develop to the adult form by late winter."
So, the answer to how long they live is long enough to reproduce a lot more grasshoppers. We suggest you get in touch with the Texas Agrilife Extension Service for Mills County. They will know more about the situation in your area, and have access to people who know much more about this than we do. The contact information for that office is at the bottom of the Home Page.