1.) You can kill all the burms you want in the everglades... it isn't going to work. You could send an army (literally, an army) in to hunt them down and kill them. You still arent going to get them all. And the volume that they reproduce in... forget about it.
2.) They are much more resistant to the cold then you think. the "massive freeze" was not cold enouph or last long enough to do any real damage to their population.