Outside of a few true rain hats, most hats are water-repellent, not waterproof. Light drizzle or a little snow won’t ruin most felt hats, but heavy rain and thunderstorms aren’t ideal. Straw hats made from natural fibers should never be worn in the rain—they won’t hold their shape.
If you do get caught out, once indoors snap the brim up and hang the hat so the sides of the brim don’t touch anything (a hat/coat rack or the back of a chair works). Let it air-dry naturally away from heat. If a hat suffers weather damage, don’t discard it—bring it to us and we’ll see what we can do.