Oilskins. Soak linen or canvas with linseed oil, let it dry. You can also treat cloth with wax, or tar, and ,later, raw rubber. All these would have problems- oilskins would tend to stick to themselves, had to be carefully hung up and stored, as did rubber ones. Tar and wax don't bear much heat.

Animal skins will shed water pretty well if the hair is left on them, too. Some military packs of the early 20th century were made of rawhide with the hair on the outside.

Heavily felted heavy weight wool (such as melton) is pretty darn waterproof. It's still used. Especially if it's still got lanolin in it (or if lanolin is added back in, which is more likely given the scouring process for wool), it goes from "very water resistant" (enough for weathering a storm) to "oh look, a diaper." Hats are traditionally made of wool, and if stiffened, it's with shellac/varnish, but coats/cloaks are also historically made of wool when they're the utility kind (as opposed to the just-for-pretty kind).