Many, many years ago (before New Fantasyland), my daughter and I were there during a very heavy rain shower in the afternoon There was no lightning. There was no line at Dumbo, and we assumed it was shut down. I just happened to ask the CM, and he told me they were open. As we were getting on, another dad and his son got on. We were the only four people on the ride. After the ride, the CM asked if we wanted to stay on since there was no one in line, which we did. The other dad and son got off. So my daughter and I were the only ones riding Dumbo. We were laughing have a great time.
During the summer, rain is predicted each day, generally in the afternoon. Bring a poncho or some other rain gear. Take advantage of the rain, since a lot of people leave, even though the rain doesn't last long.