The day I bought my annual pass this past February it started pouring rain the minute we entered the park and never let up. (The forecast was "occasional showers," yeah right!). We still had a blast, I'll never forget it. The rain made for a challenge but it was fun. Even my 2-year-old wasn't fazed. We bought rain ponchos and they helped a lot! I had dry clothes with me to change my toddler into at the end of the night for the drive home. The Enchanted Tiki Room, It's a Small World, Haunted Mansion were great for escaping the rain. Most of the rides were up and running all day, including Dumbo. And it was seriously pouring. The only one I noticed was down much of the day was Teacups. One nice side effect of the rain was people bailed as the day went on so we didn't have to wait long for rides.
For what it's worth, we have been planning on going to DL this coming Monday and we will probably still go even if it's raining.