So far I found only one reference which is not helpful
The farther into the forest, the more firewood. = As the days grow longer, the storms are stronger. тык https://translate.enacademic.com/the%20storms%20are%20stronger/en/ru/
Looks like there are two interrelated meanings here. One can be captured by the phase "out of the woods" (complexity [of the situation] as a trap in and by itself) and the second "As the days grow longer, the storms are stronger" (difficulties of any operation typically increase as your goals expand you go and you can be stack in the tar pit as the result).
BTW in the second sense it is opposite to the Russian saying "appetite comes with the meal"
Yes, Andorian is absolutely correct as for the second meaning of this saying:
As the days grow longer, the storms are stronger
It capture the "reaction part" very well, although the action part ("the farther/deeper into the forest" is the "personal action" part) is missing. But this is probably the best one can find.
Thanks a lot !!!
P.S. From Quora comment that is relevant in this context
But what it actually means, is the further you dig into some issue, the worse side effects you get, the worse collateral and the heavier the side information you dig out. It can also imply that, the deeper you dig into something, the more myths, lies and stereotypes you are bound to meet.