Believe it or not, those of us who live in FL don't stay holed up in our air conditioned houses for 6 months out of the year because it's too hot to go outside with a baby or young child. In fact, it wasn't so long ago that most Floridians didn't even have air conditioning.
As long as you take the proper precautions, young children will be fine. Since my 18 month old daughter was 6 weeks old, she and her 3 year old brother have been to SeaWorld 5 times, WDW 8 times, and on a July cruise to the Bahamas (see photo below.) Occasionally, I'm sure they do look miserable to passers-by, but the same thing happens at the grocery store, mall, or anywhere else in public.

Neither one has ever been sunburned, dehydrated, or suffered any type of heat related ailment.
My kids love going to Walt Disney World. My DS studies the park maps in between trips and plans what he wants to see the next time we go. DD gets all excited and absolutely lights up when we drive onto WDW property and she sees the purple road signs.
As a PP said, I certainly understand if people choose to avoid going with young children, but please don't judge those of us who do take our young children to WDW.
BTW, for babies too young for sunblock, you can carry them in a sling and use a Totes-style umbrella to keep the sun off of them.