Actually Steve, the male praying mantis usually doesn't live long after mating season - no thanks to his better half LOL! But yes, you are correct, the females are usually killed off in harsh winter climates, after laying their eggs.
Well, Happy New Year...
The male Mantis well expire very shortly after mating. The female will live until a killing frost or until all of her eggs have been deposited. My daughter and I raised them for a few years while she was young and it was very interesting.
This one is a male. You can tell by the size of it's head.