Yes! Yes they do.
Most grasshoppers can only survive the winter as an egg; the adults all die when it gets cold. In warm climates which don't have freezing winters, grasshoppers can probably live longer, maybe for several years. Most die long before that though, from disease or predators or drought. http://www.biokids.umich.edu/critters/Acrididae/
Roaches, on the other hand, can adapt to the cold, but will most likely die if the temperatures drop below 32 degrees.
All I'm saying is...I've lived in the midwest for my whole life and we have cockroaches that that are about the size of a penny or nickel vs living down in the south now and we have cockroaches that are about the size of a quarter or larger. :D
Thrive much? Perhaps not as well as they do in the south.
now, enough about bugs.
How 'bout them Cardinals?