If your hunting your stands just keep at it, dress warm and wear something to help keep you dry but quiet ... if still hunting keep the wind in your face. Rain can be a good thing to keep the ground quiet and maybe knock a few leaves down for you.
If you get lucky and have to blood trail a critter, mark your starting point with something the rain will not wash away and move quickly along the side of your blood trail. If it's good blood trail, my experience is you will not have an issue, but if it is sparse mark your route you go can clearly see the travel line.
Good luck