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Good news: on its own, felt is fairly water-resistant, so you're not likely ruin your hat just by getting doused unexpectedly in one storm. Using a waterproofing spray ups the resistance of your hat to make it last longer, though. With a spray, water that falls on your hat beads up and remains on the surface of the hat. Waterproof your hat after you buy it, then follow up with additional treatments as needed since the waterproofing capability does break down with time.
Read the directions on your waterproofing or water-repellent product so you know how to apply the product and how long you have to let the hat sit before wearing it.
Lay several sheets of newspaper on a table or other flat surface so you have a place to work. Place the felt hat on the newspaper.
Spray your hat with the waterproofing product. Apply the product in even layers and make sure you coat all sides on the top, or outside, of the hat.
Leave your hat to dry. Once the product sets in per the manufacturer's guidelines, you're ready to go.
Open the window to get some ventilation while you apply the waterproofing product.
Look for a product developed specifically for felt, wool or fabric. Avoid products made just for leather, Gore-Tex or other products.
You'll be able to tell when your hat's ready for another coat because the water will bead up less readily and start to soak into the felt.