Hunting in the rain is tough. The deer will move and I have no problem doing it because we get limited time in the tree. Blood trails are the limitation. 2 years ago I shot a doe and a totally unexpected rain shower popped up and washed the blood trail away. It took me 3 hours to find a deer I double lunged that ran off into some thick stuff. I got lucky because after I did find some traces of blood and followed as much as I could I lost it again. I searched and searched and finally went back to last blood and was on my hands and knees. I happened to look up and the underside of the brush's leaves was covered with blood and gave me the direction and she was just another 7 yards away.
Last year I shot another doe, similar situation. I knew the shot was perfect but couldn't see her go down as she ran into some thicker stuff. I got down right away and started tracking as the rain was washing away the blood. I found her right away.
Long story short, even with a good shot in the rain you risk losing a deer that you would otherwise find. Take good shots so you can track immediately, although it's bowhunting so there is no such thing as a gimme and any time you loose an arrow you risk not finding that deer, even more in the rain.