It depends. If it's pouring, there's no sense being out there unless you can stay dry. The deer will normally hunker down when it's raining hard, and get up to move as it stops. They will also feed earlier when they know it's going to rain, and somehow they usually do.

Don't put yourself at risk of geting sick. Also remember that if you hit one and it runs off a ways, you will be tasked with following a blood trail that is constantly being washed away. Priority one should be a quick kill, with recovery a must.

On the other hand a light rain is a great time to hunt. It quiets the woods down and also keeps your scent down, with no sun or shadows to contend with. Get a pair of yellow shooting glasses for hunting in rainy and foggy situations. They seem to increase our ability to see in this type of weather, making the deer and their movements stand out.