We took DD at 2y and 4y, in the Florida summer heat in July/August.
Both times she loved in - so much so we have been back several times since, and the heat didn't bother her one bit.
Both times we did take the pushchair. She didn't use it very much (we didn't use it at home) during the days but it was handy for her to sit in when waiting for parades and fireworks, and the trips back to the car late at night when she really was flagging - having not stopped for several hours in the parks. It was also handy for bags and changes of clothes - there is a lot of water (water play areas, fountains, etc) so good to have a towel and a rash top/thin shorts to change in and out of. You just leave them in dedicated stroller parking - never had any issues doing so and nothing ever went missing.
We did full park days and never did the part park/part at the villa/hotel. DD wanted to keep going and loved it. She wasn't really having naps by those ages, not even at 2y so wasn't really an issue anyway.
Lots of rides at all the Disney parks, and now both Universal parks have tons of stuff for smaller children including water play areas and actual rides they can go on. Once they are 89/90cm tall there is plenty.
We did SeaWorld on out first visit many years back but don't do that nowadays.
DD always enjoyed, and still does, Space Centre, and she enjoyed a day at the beach on the coast. She loved/loves the water parks too but we only do that for 2-3 hours in a morning at most as it gets too hot and busy.
The character interactions are fabulous when they are that age. At 2y DD was mesmerised by meeting her favourite princesses and other characters and it was lovely to see how excited she was.
My sister and BIL have taken my nearly 3y there today, with my parents. They flew out this morning with a very excited toddler. I'm jealous of the getting to see his reactions the first time!
DD is 14y now and still gets excited though :D