Got caught in a rainstorm about 3 miles from home on my trike conversion once. Didn't have fenders on it yet then, and I got thoroughly soaked, head to foot. No preblems from the running gear or the engine, and I had dual rear disc brakes on that trike, so I noticed no difference in braking. Cornering was always a matter of extreme care with it, but I did notice a bit of tire side slip on one corner on the wet payement.
Mostly, if it is raining, I find shelter and wait it out. Around here the rain usually comes at the 2-3 inch per hour rate or greater, but seldom lasts even an hour.