We were there at MK that morning too! We were the folks in the Mickey ponchos. I second that nothing at MK was shutdown. Beware of rides like Dumbo that have water pooling in the seats. Oddly, as far as we saw, the only ride that they made you take your ponchos off on was Space Mountain. Rain kept the crowd away, which was great.
The ponchos helped, but all of our lower halves were pretty soaked. We left at midday with the intention of going to the resort before heading back out later in the day. But once we were dry and warm we had no desire to get wet again, so we just made an ADR at our resort (Boardwalk) and ate dinner and relaxed.