I typically avoid hunting in the rain simply because I don't like being cold and miserable. However, in recent years I've made it a point of going out as soon as the rain stops or becomes bearable as I've found some very fresh and amazingly large buck tracks during this time (and hope to find one of the bucks that made them some day, preferably within 20 yards, broadside... looking the other way... heh); it seems the rain gets the big boys moving around (experienced this just a few weeks ago actually but it was unfortunately on what was only a scouting trip as it was 1 week before season opened).
FYI, I wouldn't worry so much about your feathers getting wet. I read once (possibly here) that it shouldn't make much, if any, difference to arrow flight -- we bare shaft tune our arrows after all (or should if you don't). Having wet fletching is very similar to this. The person making the statement said to give this experiment a try: soak the fletchings on an arrow and then go shoot, see what happens (shoot the wet arrows next to dry ones as well). I tried this numerous times. I was just as accurate as ever and noticed no irregularities in flight path. The only issue might arise due to high winds or other factors where fletchings help stabilize the arrow; otherwise, you shouldn't see much if any difference in the flight of the arrow so long as they're properly tuned.