First of all, nature rarely ever throw something at a population that would exterminate the whole lot if they don't change right away. Try not to watch too much science fiction movies.
But to the point. Like every population in the world, not all members of this particular population of green frogs will be completely green just like not every single member of black people have black skin. There are undoubtedly already members of this frog population with a hint of orange speckles. These members would have an advantage over the other members, and over time will become the dominant trait in the population.
But suppose we take your route. Suppose there isn't a single member of the population with orange speckles. If the change in environment is that drastic, the population will go extinct. Bye bye froggies.
Right now, you're thinking too much in one dimension. A population rarely ever have such limited traits. I live in a town of 20 thousand or so people. And even then, we have black, brown, green, white, and purple people. I've seen just about every colored eyes out there. I've also seen the very tall and the very short. What's my point? Unless there's been a severe bottleneck like what happened to the cheetahs, the probability of the population having members that have the traits to survive the environmental changes is pretty darn high.
™ Version 4.2