Hello, Julia,
June is the month we visit
Walt Disney World every year, and I'd never think twice about avoiding going because of the humidity and heat. In fact, we've had many trips that had really lovely weather. On days where it does become muggy, make sure to take advantage of mornings and evenings as they aren't as bad; those days make for good afternoons by the pools. Those warm days also often have afternoon showers that cool down the temperatures.
To also help counter days that are warmer, I really like my little personal fan or a
cooling mist fan. Similarly, cooling towels like Frogg Toggs can be incredible to bring some cool relief when needed. We find Disney's Animal Kingdom always a bit more humid, so we usually bring those along with us there. Many of the queues at attractions are in the shade or even inside, so that helps, too. Not to mention, many attractions and restaurants are also inside with air conditioning. So even if it is hot and humid, you won't be spending the entire day in the sun. Also, you can ask for a free glass of ice water at any of the counter service restaurants, which helps to stay hydrated and cooled down. Of course, make sure to wear plenty of sunscreen as the sun's intensity can catch guests off-guard.
To help you know the actual temperatures in June, the average low is 71 and average high is 91 with an average daily temperature of 81 degrees. The humidity is 70% (October is 75%!). For my family, June works, but it doesn't mean it will for everyone else. I want you to have the best trip possible, so you'll want to do what works best for you.
If we can help with any further questions, please let us know. -
Kara