I know if it's raining out, and you start to hear bird song, it means the rain is about to stop.

Also if leaves on trees are flipped upside down, it's about to start raining.

Do with that what you will.

They used "weather ropes", which was a rope hung outside every night before bed. When they woke up, they would bring the rope inside and look at it. Wet meant rainy, cold meant cold, hard as a rock meant really cold, and if the rope was missing, that meant it was windy.

Edit: ok, that was fun, here's a real answer: https://academic.oup.com/edited-volume/43505/chapter/364127476?login=false

tl;dr: they made observations and created almanacs. A combination of the two was usually "good enough". No mention of war in anything I was able to find, but I'm sure it was just as large a factor as it's always been. The Art of War was written like 5,000 years ago and talks about considering the weather, so it was definitely something humans had been doing for a while.

effect [...] wars

Do you mean

• affect, as in to cause a change to; or
• effect, like "effect a limp"

If Asterix taught me anything, birds flying low meant rain was coming.

What did they do? Probably some involved and esoteric sacrifice rite or omens. Did it work? Probably not.

Their religious habits and their fortune telling had a huge influence on everything they did and every time anything went wrong, somebody would claim because somebody else ignored or misinterpreted a bad omen or the holy chickens not eating.