When you plan your trip to Walt Disney World months before you actually go down for the vacation, you probably envision a beautiful day with a few white puffy clouds off in the distance with the sun shining through on you and the people you're on vacation with; A day so nice that they ought to make a postcard out of it (if they haven't already). Despite these grand dreams, we have no control of the weather (despite my best efforts) and what can often occur is a "rainy day". Dealing with a rainy day can be a challenge at any theme park but in terms of the Studios, hope is not lost.
First, let's define what rain is. In Florida, we have two types of rain. On the one hand you have the passing thunderstorm, which can last anywhere from a few minutes to a few hours and they usually occur in the afternoon (especially in the summer). The rain can be very heavy at times and it usually brings with it lightning and thunder. On the other hand, we have your rainy day where it literally rains all day. There may be breaks in the rain, but generally speaking from park opening to park closing it looks like it's going to rain (if it isn't already) and breaks from the rain are the exception.
Hollywood Studios' small size in terms of park acreage works to your benefit in terms of dealing with rain. The big issue for folks to deal with the rain is being outside in it means you get wet and that's annoying and no one wants that. I know that sounds trivial but the reality is people can deal with a little rain but a lot ruins days. The first thing most guests do when it rains is panic. They run for cover and if it doesn't look promising (as in it wont let up in the next 90 seconds), many consider abandoning all hope for a day in the park and to head out. I've seen the deluge of guests out the park gates because of some rain and you should know that rain isn't a reason to skip the park and go back to your room for the rest of the day to watch classic Disney cartoons.
Rain mainly affects the outdoor attractions. Light rain won't do much to any attraction (especially if it's sporadic). Since we're not really talking about that kind of rain, let's focus on the regular to heavy rain. The attractions most affected by rain are going to be Lights, Motors, Action! Extreme Stunt Show, Honey, I Shrunk the Kids! and Fantasmic!. These outdoor attractions will close (mostly temporarily) when it's raining. Character meet-n-greets and other outdoor entertainment (Streetmosphere, Jedi Training Academy, High School Musical 3 Pep Rally, etc) will also be canceled or delayed due to rain. Lights, Motors, Action and Fantasmic! are the most affected by it and Disney will often cancel showings, especially when lightning is involved. If these are canceled, there's not much you can do except come back another day to see them. There are other attractions that are not totally indoors (Beauty & the Beast, Indiana Jones Epic Stunt Spectacular, et al) but they are covered and not affected by the rain generally.
Your key is going to be braving the elements and walking around while it's raining. The advantage of a rainy day is you can plan on it raining all day and therefore bring things with you to make it easier on you. On the other hand, when it suddenly rains in the afternoon, many guests are caught off guard. The best "tool" to have with you if it rains is a poncho. Disney sells them for about $5 nearly everywhere once it rains (just ask if you don't see them out). They're plastic and clear and they do a good job of keeping your clothes dry. You can even bring your arms inside of them to keep those dry. Ideally you should combine the poncho with an umbrella. Ponchos are great but you're still getting rained on when you're outside. Bring an umbrella along with the poncho and now you've got the rain out of your face (literally) and it can make a big difference in being able to enjoy yourself.
Touring the park isn't much different when it comes to rain but there are some general tips you can keep in mind when trying to do it all when it's raining. To your benefit, when it rains many guests stop or leave. If it's a passing storm, guests stay where they are and many wait it out until the rain stops. If it's an all day rain, many guests don't even go to the parks, not wanting to deal with the rain. Take advantage of this because wait times around the park will diminish somewhat due to the rain, especially when a passing storm doesn't pass so quickly. It's a great time to ride a headliner attraction when it rains since many are stuck or have left.
Most attractions have the benefit that once you enter the queue, you're indoors (or at least in a covered area) and out of the rain. On the tram on the Backlot Tour, you can still get wet since the vehicles are covered but only from above so rain can come in from the side. You may want to keep your poncho on since seats can get a little wet regardless of attraction.
When it rains, it's a perfect opportunity to scavenge for dining reservations. Many guests make their Advanced Dining Reservations (ADR's) back home when they were still dreaming about that postcard moment in the park. When it suddenly rains and the kids are crying and everyone is wet, they leave and abandon their ADR. This is a great opportunity for you to try walking up to your favorite sit down restaurant at the Studios and seeing if there is availability now that some guests have not shown up for their reservations because of the rain. I've run into Cast Members who have been helpful and let me in because of this while I've also run into Cast Members who stick with the ADR's that they have booked. It's worth trying certainly and the worst thing that happens is the Cast Member says nothing is available. Additionally, if it's a rainy day, guests will sometimes call ahead and cancel ADR's the day of their reservation and you may consider calling into the WDW Dining hot line during the day to grab an opening slot. Give it a shot and you may find yourself able to sneak in somewhere you previously thought was booked up.
Let's say you find yourself in one of those surprise afternoon showers and you forgot your poncho at home and have no umbrella. What to do? I would consider an attraction that has a long ride time such as the Great Movie Ride, Backlot Tour or Beauty and the Beast. Alternatively, try out the previous tip of trying to grab a spot for a meal. And if all else fails, get on the standby line for an attraction with a longer wait than you might usually wait on (i.e. a headliner attraction). Sure the wait is long, but you may as well wait around for a ride than just wait around for the weather to change. Lastly, if you're looking for a place to just sit down and relax and wait for the rain to pass without getting wet, try the ABC Commissary; it's large indoor space means there's bound to be a table to sit at and you can clearly see outside to see when the rain will stop with easy indoor access to food, beverages and a restroom.
The bottom line is that rain isn't a reason to run out of the Studios. Use the bad weather to your advantage and keep touring. With the right gear and know-how, you can still have a productive day at the parks and see many of the attractions the park has to offer despite the falling rain. Besides, it's not like you're going to melt from the rain, right?