As others have said, on Splash Mountain if you put your feet on the braces on the sides of the log, way up high under the top lip of the log, your feet should say quite dry even if the rest of you gets wet. This may not work if the log you ride in is very heavy.
On GRR, there are holes in the bottom of each boat where water can shoot up. If you put your feet over the holes closest to you, it can keep your feet dry. This works well if you do it, but doing it is the problem -- I have gotten into the ride so much that I forget to cover the holes and then suffer for it for the rest of the day.