There are plenty of cold-blooded species that live in places that freeze in the winter, notably including all plants. So somehow your logic has a flaw.
Yeah, that's a classic. Always reminds me of the Sugar Barons of Hawaii importing Asian mongooses to handle their rat problem; sadly, the rats are nocturnal, and the mongooses are diurnal. Also tasty are groundnesting birds. Oops.
Skinner: Well, I was wrong; the lizards are a godsend.
Lisa: But isn't that a bit short-sighted? What happens when we're overrun by lizards?
Skinner: No problem. We simply release wave after wave of Chinese needle snakes. They'll wipe out the lizards.
Lisa: But aren't the snakes even worse?
Skinner: Yes, but we're prepared for that. We've lined up a fabulous type of gorilla that thrives on snake meat.
Lisa: But then we're stuck with gorillas!
Skinner: No, that's the beautiful part. When wintertime rolls around, the gorillas simply freeze to death.