I like a light rain.
Don't wait to track your game like you would on a dry day. Go after him,,, it's slow, quite going until you find it down or give a follow up shot.
Deer will get your scent easier in moist weather so always play the wind while huntinf or following up a trail.
One good thing about rain on public lands,,, you're usually the only one out there!
Even without proper rain gear in a light rain, I can tough it out most of the day if it is above freezing.
I will also ground hunt more than tree standing in the rain. A good time to still hunt and slip around the woods. Even if you don't slip up on something as stated above,,, it's a good time to scout new areas.