My opinion...light rain=no big deal, steady rain=much less fun, downpour, monsoon=fun again. In the first scenario it's easy to dry discs enough to throw them. In the second scenario it's possible sometimes, but it can get tedious. In the third scenario, you know it's not even worth it and you don't care. Chuck that soggy plastic!
In all scenarios, watch your footing. You probably won't be able to absolutely crush the disc like you would on dry ground...esp. if it's muddy. Sometimes you just need to stand and deliver if it's really bad. I can usually get away with a slow walk up in all but the muddiest lies.
I wear a raincoat that allows my arms to move freely. Under this I usually have one or two teeshirts on. Then I keep a towel tucked under it to keep dry. I use the towel to dry discs and when that is too wet, I start using parts of the teeshirt. I actally bring a couple of towels in ziplock bags to change out when one is wet though. And here's the biggest tip (that may be obvious): ONLY DRY THE PART OF THE DISC YOU ARE GOING TO GRIP. Don't waste time drying the whole thing or keeping it dry in your bag. Dry that part, then grip the disc how you're going to throw it. Approach your lie and let it go. This requires you to be decisive about what disc you're going to throw before you start drying it.
The only other advice I have is this regards wet feet. I hate wet feet when I golf. I wish I had purchased waterproof shoes. Instead I'm still stuck with my BITE shoes that said they were "All weather." They are not waterproof. I do have to say they have great traction for muddy terrain, but still a disappointment for me. Anyway, if you're like me wihout waterproof shoes, then get a pair of Smartwool socks. Merino wool is the more generic name for the material. You can pay less for a nonsmartwool brand, but they often won't last as long. Anyway, the awesome thing about wearing your 8-18 dollar pair of socks is that the material does get wet, but when it's wet it still insulates and keeps your feet warm AND it won't chaff your foot and give you blisters. Cotton socks completly suck when they get wet. You'll have blisters at the end of the round and if it's cold your feet'll be numb. There's a mountaineer motto that says: "Cotton kills." In the mountains this can certainly be true because it takes soo long to dry and insulates poorly, but in disc golf "Cotton is really really annoying."
The only rule I go by is...DRY FEET. so far this rainy season my seal skins have been well worth the 30 bucks they cost. washed and dried properly they will keep your feet much happier. I stood ankle deep in a creek because the walls would not allow me to stand anywhere else. Shoes got soaked, feet stayed dry
Playing in the rain is can be alot of fun, and add a challenge to your game. Just make sure that you have a good, pair of shoes that will let the water stay away from your feet and not soak it up so much. A golf umbrella isn't a bad Idea, a few seasons back I even purchases a rain coat to keep me dry when I was playing in the rain. Don't let a little rain stop you get out there and have fun.
cold rain, not worth it for me because the raincoat or plastic is very cumbersome. Summer or (warmer) rain? waterproof shoes, and a dry towel. I like to keep atowel in a plastic bag and will keep my throwing hand squeezed on the towel so my hand doesn't get all puffed and wrinkly. As for the rest of you, let it go, fighting the wet will make it worse, I wear a baseball hat so it stays off my face but once your body is wet you won't even notice. WAY FUN!!! Especially with FLX plastic.