I have a set of russel APX rain gear. Great stuff, super light, quiet, and waterproof. Combined with a set of Alpha burly 2 boots and a hat that will shed the worst of it off your head without going down the back of your neck. Also prone to wear wool underneath and even add a tarp style poncho when its really coming down. Some times its just about impossible to stay dry. Sometimes boot foot waders and poncho is about the only way to stay dry.
As to feathers its tough, I have used plastic bag over my fletching, and tried spray waterproofing like camp dry. Probably a quiver like the simmons bushmaster or other covered bottom feed quiver would work well also. Make sure to put something on your broad heads. I like using thompson bore butter, a food grade lubricant they sell for muzzle loaders. I have a PVC pipe style arrow case that keeps them dry while I'm not hunting. You can take 6-12 arrows in the case and only bring out 4 at a time fork my bow quiver, that keeps dry arrows available for the duration of the hunt. Drying them and steaming feathers back at camp is fairly common
With my 2pc T/D longbow I have a 4" pvc pipe case that will hold the bow and a half dozen arrows to keep the hole thing dry until ready to hunt. Also about the only way to not break a bow on a 4 wheeler trek back to hunting grounds.
Make sure your arrows are as well tuned as possible. A well tuned arrow will shoot good even with wet feathers. 5" shield cut soaking wet on my arrows shoot fine.
I use thin calf hide tabs and keep one in my water proof zippered pocket to keep it dry.