Yes, wet feathers do have a bad effect on speed and accuracy. How much of an effect depends, as noted above, on how well the bow is tuned and how good your form and release are. I've never had much of a problem keeping my feathers dry. Until those gallon size baggies cam out, I just used old bread sacks to cover up my feathers in the rain.

Covering them up is your main defense against wet feathers. Waterproofing agents are your second line of defense. If you're caught in a downburst, deer aren't going to be moving anyway, so stick your ready arrow in the quiver and cover it up with the rest of 'em. You'll have more problems on wet, foggy, drizzly days because deer are going to be everywhere on a day like that. I just switch to a fresh ready arrow when it looks like the mist has penetrated my waterproofing on the arrow I've had out.

A friend went to England some years back - many years now, come to think of it - and brought back a package of goose feathers for me. They were amazing, how well they shed water. No wonder so many authors and poets refer to archers' "gray goose quill shafts." They were very good fletches.