The exotics here are not immuned but are tolerant of cold weather since each generation gets stronger as the weaker die and the stronger survive.
Years ago aprox. every 3 to 6 years South Florida would experience a freeze and large amounts of iguanas and other exotic species would die off. The survivors would live on to re-produce.
The "problem" we have with both the common Iguana, spinney-tails (Similis and Pectinata)is that they hide in structures, thick palm trees, and underground therfore they are not directly exposed to the cold weather. Only some adults and a lot of babies that have not found shelter are vonerable. In addition they have very few predetors and these animals have a high reproductive rate. This has caused a population explosion which is out of control.