How wet do you need to get it? All Gone Country hats are treated so that they can get wet and recover. Our western fashion hats will shed water but you don't want to keep them soaking wet if you can help it. Palm straw cowboy hats are made to get really wet. Swim in them if you want to. Wear them at a festival even if it pours all day. The lacquer will soften and they'll feel a little sticky, but once they dry they will be back to good as new. Just re-shape them while they are wet and make sure not to let the brim flatten out. Dry them completely as soon as possible so they don't mildew. See here how to keep them in their best shape. The Smokin Black is treated to be absolutely waterproof. You can wear it in the rain for days and it will retain its shape and the color will not run.
Felt hats can get wet, but they are not made to be wet for long periods. If you get caught in the rain in a wool or cotton felt hat, pat the water off and let it dry. If you keep your felt hat brushed clean it will not water spot too much. As with any hat, never put it away wet.