This is a valid question, and one everyone should consider.
I`d never bow hunt in the rain intentionally, just because the blood trail is so important in bow hunting especially.
One hunt, after I had shot what turned out to be a very big button buck, as I was sitting in the stand, giving him time to lay down, the sky to the west grew black, and the thunder began to rumble. I was torn. I didn`t want to lose the blood trail, but more more concerned with pushing him and losing him anyway. I waited in the stand, and it began to rain. Washed the blood from my arrow, washed away any blood he had left behind. I looked for an hour, and found nothing. I called my nephew, and he came back later with me, and we were fortunate enough to finally find that pretty deer.
It wasn`t raining when I shot, and the weather seemed to come out of nowhere. I don`t ever want to deal with that feeling again.