You think you get it bad at WDW, try walking around the sidewalks of NYC for a full day in the heat. I started going to NYC every summer when I was in my 20s, thin, and in good shape (blows the 40 and fat theory). I do have fair and sensitive skin. Every time we spent the day walking the streets and exploring, I would get this over a good part of my lower legs. It does burn or itch a little. Most of it would be gone by the next morning, and within 2 days, it would all be gone. I just assumed it was from the steam and dirt on the NYC streets and sidewalks. I figured the steam coming up from the pavement was probably tinged with all types of dirt that aggravated my sensitive skin. At WDW, I do occasionally get a little bit of it, but nothing like I did when we were going to NYC every year. At WDW, it is almost always gone by morning. I just figured it was the dirt from the ground, and the rubbing up against all kinds of surfaces from rides, sitting on the ground for parades, etc. It definitely isn't bug bites or anything like that. It is just some sort of allergic skin reaction to the heat and pavement. I'm surprised from this thread to see how common it really is!
Oh- just to add- I use cortizone on it which seems to take care of it. I think I have tried Benedryl too and I think that worked. Definitely chlorine and water are not a factor- no getting wet in NYC- and No bed bugs or other bug bites- stayed at inlaws for NYC trips. I don't get swollen feet or ankles. Can't say whether the chemicals in sunscreen would have played a part, but I doubt it.