For the last 6 years all my logs have been stored outside. They get wet when it’s wet, they dry when it’s dry. Even when it’s really wet only the outer logs see any water, two rows down they’re bone dry.
I’m currently working my way though a pile that were stacked in the open in 2013, they’re fine.
I have a small store that I keep topped up with dry logs, so if it ever rained for weeks on end I won’t be stuck.
I will build wood sheds one day but purely for convenience – so I don’t have to stack them tidily and then keep moving wood about before use. If it’s all under cover I can sling it in once, pull it out once. Rather than having to shift logs on dry days into the ‘tertiary’ store IYSWIM.
So rain water on logs? Not a problem.
Personally, I never burn wood unless it’s bone dry but maybe that’s a bit OCD.