I actually enjoy hunting in the rain. I have called several in the rain. One with a snow on the ground an freezing rain falling, one in an outright downpour. My theory is that they are out there somewhere, you just have to find where. The wet ground makes it easier to sneak in close to the bedding areas undetected. The sound of the falling rain can also cover the sound of your steps. Most of the time you have the woods to yourself too.
One morning around 4am, my dogs woke me up wanting to go outside. I reluctlantly let them out because it was pouring the rain. One of them barked at something in the yard and this set the coyotes off. They were in the field across the road from my house and they were tearing it up.
To us humans it is natural for us to want to go inside during inclimate weather. To coyotes and other animals it's just a way of life. I really don't think it matters to them. They gotta eat no matter the weather. Watch the other wildlife. Turkey, crows, geese, even deer and you'll see them active during rain. I like to hunt. If I have the urge to go I don't let the weather stop me. Just enjoy it...