I've done it...I'm sure I'll do it again. Won't do it in a downpour of course, but I won't stop hunting if it starts drizzling. How cold and windy can be a factor too-nothing worse than being miserable cold AND wet!
I've hunted in all types of rain from mist to downpour. Can't say I ever did very well under any of those conditions. The birds sure don't seem to want to fly IF you can find them.
Do I still do it? Yeah. You can't get any sitting in front of the fireplace or TV. After all, I'm out there to hunt. Dogs never seem to mind anyway.
AFTER a rain is one of my favorite times to hunt. The roosters will leave the trees (or whatever they were using to stay dry) & find the lightest cover they can to dry off (yet heavy enough to stay warm & protected if necessary). And they'll minimize their time feeding due to the mud. They don't like muddy feet any more than I do. And....scenting conditions can be phenomenal!
Pheasants are a dry feather bird. They want to keep their feathers dry because it is hard for them to fly with wet feathers. So look for them to hide in and under places where thy can stay dry. Trees, cedars, tree rows, etc.