As long as the shafts are sealed properly, like several dips of lacquer, the rain shouldn't hurt woodies.Most all the arrow builders put plenty of lacquer on their arrows, but some of the less expensive ones have probably skimped to save money.

The two areas you need to take special notice of are the tapers at the nock and point where the seal coating is removed during tapering. Find a paint, polyurethane or lacquer that is compatible with whatever was used to seal the shafts and use an art brush to paint any exposed wood after you've installed the nocks and points.

Another thing I do with my arrows is to use a silicone based automotive paste wax, like Kit,on the first 10" or so at the point end of my arrows. Rub it on, then buff it off. That cuts the friction from the targets so my lacquer doesn't wear off very fast. Not to mention making them easier to pull from 3D targets. And the wax also helps keep water out of the point taper, just in case.

Oh, another thing... If you're worried about whether you've got your arrows sealed, you can weigh them on a dry day and on a rainy day. If they get heavier in high humidity, then they are absorbing humidity from the air. That means they are not well sealed.