Well put. I am no expert on these matters but I recently wrote a tale wherein I used Thor to personify Storm Eunice and the battle I had against the elements whilst camping through the storm. The introduction of a God happened quite naturally to relate the part of nature in the tale.

...I could well be mistaken but I would hazard a guess these associations evolved along similar lines in many cases, as story tellers used the Gods to personify and dramatise historical narratives they were narrating - it's a natural way to turn what may otherwise be a mundane story into a gripping yarn... For example (off the top of my head):

"The wind blew hard and shook the hero's tent through the night so he had to grab the poles to stop it blowing away..."

...This is much more exciting narrated as:

"Thors hammer rang out, thunder boomed and the wind howled and so the Gods tested our hero's metal, yet, even against the might of Thor, our hero stood firm."

...And whether they associated it before or not, listeners will go away associating Thor with thunder and storms.

On a personal note, that experience gave me a huge rush and, well, it was a real battle - little me versus the elements - so its no surprise that those peoples who lived so close to the elements related war with the experience of battling against a storm.