After rain gets wood wet and soaked it can take from 24 to 48 hours to dry back out.
Of course it can take a bit longer for the wood do dry back out if the weather is damp and cloudy but if it's sunny and warm or sunny and hot then the wood will dry out much quicker.
Whether it's lumber or firewood you're talking about you should keep both of them under cover when it rains.
So if you're planning on burning firewood and it's gonna be raining or snowing you should put a tarp over the firewood pile to prevent it from getting wet and then remove the tarp after rain to allow it to dry out because the firewood will still get a little bit wet.
Keeping lumber dry and under tarp or inside a building if possible is best to keep the water off the wood to prevent the boards from being warped.