In general, rain, or water in general, will not permanently damage a paintball gun. Some guns, such as those that have electronic circuit boards that are not protected, could potentially have problems, but most will do fine.
Water on a paintball gun, particularly a mechanical gun like a Tippmann 98 or a Spyder, will not hurt the gun. There is the possibility that leaving the gun wet (such as dropping a wet gun in a gear bag and forgetting about it) will lead to rust which can hurt the guns performance. In the short term, water will not hurt the gun. Simply dry off the gun and you should be good to go.
One note to keep in mind with water is that, while it will not generally harm your gun in the short term, it will do a number on your paintballs. Paintballs that get even a little wet will begin to swell to the point they don't fit down your feed tube, will break in your hopper and will warp or dimple. If you can keep your paint dry, you can play paintball in the rain.