First realize that firewood has two qualities when it relates to moisture.
When a tree is cut down the wood is green. Over time the wood seasons, natural moisture in it evaporates. Depending on the type of wood, it takes 6 to 12 months to become seasoned. Green wood will burn, but it spends most of its energy boiling off the moisture in it and does not provided as much heat (chimney concerns are out of scope for this answer)
Seasoned wood that is sitting in water will get wet, and won't burn well. Much like green wood, it can burn assuming it is not waterlogged. A passing rain is not going to have a significant impact on firewood that is not laying in a puddle.
Storing your fire wood for winter use. Cut and split it to length, if the bark stays on the wood leave it on (best), if not set the bark to the side. Put something down to keep the wood off the ground (foundation), such as rocks, large branches, a pallet, or a couple of pieces of firewood (set at a right angle to the stack). Stack the wood bark side up. Essentially you are building a bark roof. If the bark came off you can use it to cover the pile and a use the same type of things used for the foundation to secure the roof.
For the most part the bark will shed the rain and the snow, the foundation will keep it from soaking up water, and the open ends, and splits will help it season faster.
Image shows a well built wood stack.