Well Evolution Requires Either Genetic Drift Or Selective Pressure
Dealing with environmental changes has certainly driven evolution on Earth. The key thing I think is that the change has to be gradual compared to reproduction rate. I'd guess on the same order or longer than the generation time. Too fast and a population is wiped out before it can adapt. A creature can't deal with climate extremes in it's on lifetime without migration so there has to be a safe place to go in the event of rapid weather changes along with some predictability or an ability to detect the change in advance.