Given that there's no parade music and no other performers on foot, it looks to me like they were caught out by a sudden storm. It looks like all the 'foot' performers have left the parade to safety, but the floats have to continue along the route to get backstage. The characters that are left are the ones that cannot get down easily, so they just have to ride it out...
Edit: If I recall correctly, doesn't TDL have a special Rainy Day Parade? The fact that they do (if it's true), and this wasn't it, also suggests that maybe they just got caught out this time.
I guess there must be an assessment somewhere along the line of the risk of keeping the characters on the floats and getting them backstage ASAP, versus trying to get them all down off the floats in the middle of the park - from a wet and slippery float, in full costume, and without whatever stairs/equipment they normally use.