Great time to still hunt! As others have said, if you arrows are tuned the wet feathers won't hurt much.
I am going to get hammered here but as far as rain washing away blood trails...it happens.
I try to be as ethical as possible, but you can "ethical" yourself into never getting a shot or making a kill. And if the rain helps you get a shot..Take It!
"The (deer, hog, etc...) was too far...too alert..too much rain...not quartering away....etc...
Yeah it sucks to lose an animal, but it isn't wasted. Compensatory Mortality, if you don't shoot it it will die of something else.
Rain is great time to hunt or fish. (especially since no one else will be out there and it is so nice to have the woods to yourself) OK, let me have it!
John