In general "rain" will not close down much. Lightning will close down all outdoor attractions (Big Thunder, Splash, Autopia, Storybook Land, etc). The extend of the rain will determine whether the parade will run. If it is a light drizzle they will usually run it, if it is a steady downpour or if there is lightning they will not. It really just depends on the rain. If they feel that you or the cast is in danger of being hurt they will shut outdoor entertainment/attractions down, but there is plenty of indoor attractions, merchandise locations and food locations that you can go to if that does happen. Keep in mind that DL does not get nearly as much rain as WDW...I have been to DL many times (to many to count) and it has only rained on us once...everything was up and running as it was just a rain day (no lightning and not to hard).