Waterproof socks/ pants/ jacket
hat (nothing's worse than rain drops in the eye)
Tripod stool (to keep my bag off the wet ground)
ziploc baggy (to keep small things dry like scorecards)
beanie bag (helps dry fingers/disc to get grip)
Its taken me 5 years or so to figure out I needed all this stuff even though the first tournament I played in, it rained/poured on us the whole 2nd day. Great question. Wish I would've asked sooner.
Ken Climo in the Atlanta Open video showed a trick: in between rounds, go in your car and put your towel (or probably other gear you want to dry) on the defroster vents and then crank up the heat. Said it dries off the towel in 5 minutes. I haven't tried it, but hey, he won that tournament!
Also, I wear a waterproof jacket and when the towel is wet to the point of being un-usable I am usually wearing a cotton tee shirt under the jacket that stays dry. I just use the tee shirt to dry off the discs, going up under the bottom of the jacket. AND when I dry my discs in order to throw, I only dry off the area that my hand is gripping. I think this keeps your towel/shirt from getting saturated as quickly.
This year I'm going to start bringing extra socks...smart wool feels pretty good even when wet.
I like a poncho better than a rain jacket or umbrella. More room and better freedom of movement than a rain jacket and what do you do with the unbrella while you are throwing? Rain pants to keep the legs dry and your favorite foot wear for wet conditions. Ball cap so that the hood turns with your head or a wide brim hat worn with hood down .
I am using a cart for my bag and it has a cover for my bag, but if you carry your bag using quad shock straps, get a backpacking poncho. This will keep you dry and you can layer your clothing for cool weather.
Sham-wow for the discs, and dry towels for the hands.
Usually carry four dry towels, in zip-lock baggies in case the rain really comes down.
Rain gear and an umbrella to stay as dry and comfortable as possible.
Seal skins over dry socks and a change of both just in case.
The hats a must, nothing worse than a wet head and raindrops in the eyes.