Yes, it definitely stays the same. However, Dudley Do Right is always in refurb during the winter time, at least it seems it is whenever I'm there during that time. PopEye has refurbs during that time sometimes, but I'm not sure if it's as long as Dudley Do Right. Jurassic Park is always open due to the fact that it's not as intense when it comes to getting wet as the other rides.
It's kind of hard to make a ride that gets you "less wet" when it's already designed a certain way.