It doesn't matter how slowly things change. It doesn't matter how big the inputs are. Complex dynamics teaches us that scale does not matter; very small inputs can and do end up being more important than very large inputs.
I'll say it again: scale does not matter.
No, they cannot tell if a season is going bad well ahead of time. It is a fallacy to think that they can. They can tell that a season is going bad exactly at the moment the season starts to go bad.
Why is it that every time I raise the issue of the unknowable future of chaotic systems that people down-vote me? Is it so hard for you to accept? Check the math and the science: it is sound. I am sorry you do not like it, but the mathematics of chaos is not some fringe idea. It underlies everything. I'm astonished that so few people have noticed this.
For example, here's an article I just found on modeling stochastic nonlinear dynamics in ecological/oceanographic applications: http://arxiv.org/pdf/1211.1717.pdf
As for caterpillars predicting climate patterns, I agree with you that it's unlikely, unless there are some simple environmental indicators the caterpillars learnt/evolved to take into account but we humans haven't paid attention to yet. This doesn't mean the changes are unknowable.
Proof needed.
e.g., the UK Met office predicted this would be a dry winter...
How about applying some statistics, like the probability that a correct forecast (whatever that is) could be accounted for by chance, given the population of forecasts and conditions in which it takes place? P-values have their limitations, but that's no reason to discard them entirely.
Edit: It says this right in the article: climate forecasters focus on things that change more slowly, such as temperatures of the land and oceans... they try to say whether a given three-month period will be wetter, drier, hotter, or colder than average.