Many cliff faces have overhangs where the rain can't reach you, and you can often make progress by climbing underneath these and leaping onto the top once you get high enough. If the ground is level enough you should be able to make a campfire under these outcroppings as well, and you can choose to wait out the storm once it's lit. Speed elixirs, stamina elixirs, and climbing gear go a long way to aiding in rain climbs. Revali's Gale has been brought up already but once you have it, rain is virtually a non-issue. You may rarely be blocked by rainfall. I played the game for nearly 300 hours and there were maybe 3 times I felt I needed to wait out a storm. Every other time I was able to either find a way up or around to wherever I was headed. Even short hops between inclines was enough to make it up good-sized mountains during rain. Sometimes I used octo-balloons to raise platforms high enough for me to leap off of, to climb to safe areas. It's a fun mechanic. Thunderstorms give you the opportunity to turn the elements against your enemies. All rain types give you penalty-free shield surfing. You're sometimes forced to re-think your navigation or switch your equipment, but that's only a good thing as far as I'm concerned. We play these games to overcome challenges that are presented to us. Developing on-the-fly solutions and scrapping through dynamic problems are BotW's greatest strength.
I wonder how methods of overcoming rain could be presented without spoiling the experience. In BotW, you experiment to find solutions. It resonates so much with me because it doesn't tell how to solve the puzzles it throws. You develop your own ad hoc solutions to whatever situation presents itself. If it were to more explicitly say "here is how you can bypass this obstacle," I think it would lose much of what makes it special.
It seems like there is a definite "wrong" way to play, though. And that's a shame. Waiting out rain is the worst solution to the problem. But it's also the most obvious. Likewise for avoiding broken weapons: many players choose to avoid combat, because they don't want to lose supplies. But the only way to get better supplies, and to increase the durability of drops, is to expend supplies and engage in combat. For those who play the "right" way, these systems become obvious hours in. But those who choose to play conservatively never even get the chance to discover they're doing something wrong. They just slog through. Nothing improves for them because novel discoveries can't be made. The game gives you the freedom to ignore its systems, which results in an inscrutable experience if a player doesn't push far enough in the right direction.
The thing is, that seems like an unavoidable consequence of being hands-off. It's a carefully crafted experience, and the development team must have known the risk involved with allowing the player to miss so much. But I think they made the right decision. The critical and fan reception was overwhelmingly positive, and it's sold so well that I'm confident in saying most agree.
