Throwing in the rain is not ideal but a reality from time to time during the season. Practicing in the rain is essential to learning how to maintain good body positions throughout your throws. Yes, you must slow down, however maintaining balance over each phase of the throw is critical to throwing well on wet or fast circles.
I had a great opportunity to talk with Mac Wilkens, former Olympic Champion and U.S. record holder in the discus, about how he approached throwing in the rain and he had some interesting points of view. His advice was to "SLOW DOWN!" "If you are 150' discus thrower - slow down and hit good positions. Try to start with a comfortable warm-up throw of 120'." Then add speed as you feel comfortable. 'Slipping, falling down, or throwing out of bounds going full speed doesn't tell you anything you didn't already know. Build up your speed and aggressiveness slowly and you will be more confident in a wet circle.' Great wisdom from a great thrower.
Weather, especially in the discus, be it rain or wind, can really have a huge impact on distance. Some days the weather might dictate if you can throw for a P.R. or if you must just focus on competing in the elements given. If you can remember this when you train in the rain you could be preparing yourself for an important meet that may have terrible weather in the future.
If you know its going to rain a couple days out from a big meet...try dumping a bucket of water in your circle at practice and throw in conditions similar to the real thing. Shoot some video of your wet circle throws and see if you are maintaining good positions. If you lower your center of gravity by bending your knees a bit more than usual you might see that you can maintain better control. If you see you are slipping and falling all over the place - check the video: is your upperbody doing more work than your lower body? Or you might be falling because you are not keeping your center of gravity over your knees and feet.
Practice throwing in less than ideal weather and you may surprise yourself at the confidence you can build-up. You may even catch your opponents off guard.