Generally there are 2 possible conditions that people conflate as "the Disney rash". The most common is exercise-induced vasculitis, which as noted above, comes from unaccustomed walking in warm weather. The giveaway for this one is that if you are wearing socks, the rash will normally form a line where the sock tops are. (This is because the socks cause compression of those small blood vessels, which helps to suppress the swelling.) The best treatment for it is cool compresses, cool foot baths, & elevating your feet. Aloe vera will usually cut down on the burning sensation. Taking NSAIDS ahead of time helps some people. Wearing long pants won't prevent it. It happens most often to people who don't spend much time on their feet, so getting into the habit of walking before a trip will usually help.
The other cause is Polymorphic Light Eruption (PMLE), which is caused by unaccustomed exposure to UV-A radiation. It most commonly happens to people who are fair-complected, and most commonly when they travel from a colder climate to a warm one. Wearing long pants WILL help to prevent this one, *if* the fabric is rated to filter UV-A. (Many sunscreens work only against UV-B, so sunscreen has to be the right kind, too.) In this case, "hardening" by getting gradual exposure to UV-A before you travel (either sunlight or artificial sunlamps) tends to help most, and an anti-histamine taken ahead of time may help as well.
If you are out-of-shape AND fair-complected, it is possible to get a combination of both conditions, which becomes especially hard to treat effectively. Usually they will fade away completely on their own within 2 weeks of getting away from the situation that caused them.
IME, prevention is more effective for both of them.