I've had a fireplace in the past, don't have one now (Yes, they DO have fireplaces in FL!). I tried keeping firewood in the small holder near the fireplace and found it wasn't a good idea. Almost all seasoned wood will have critters of some sort under the bark or in the wood. As Newfie said, I ended up only bringing in enough for a day or two when I was going to have a fire.
Pesticides on firewood is not a good idea, either. The smell of burning poison isn't quite the same as burning clean wood.
Rain won't necessarily mess up firewood, surface moisture dries off quickly when you start your fire. I have always recommended keeping firewood outside,uncovered, usually at least 3-5 feet away from the house. Not stacked against it. Don't cover it with plastic or a tarp, that will contain moisture and not let the sun and air dry out the wood. Under a lean-to or in a shed is the best, as long as there is plenty of airflow to let it dry out.