My son was 3 on our second trip (full disclosure: trip was the last few days of May/first few days of June, and he turned 4 on July 27, so he was an "old" 3). He LOVED it. He's skinny and tall for his age, so he met the 40" height requirement, and I have some PRICELESS ride photos of him from Splash Mountain, DINOSAUR, Haunted Mansion, and Frozen. I've found that, with him at least, taking him on those rides as a small child and not hyping them up beforehand as something to be scared of actually led to him really enjoying them. He's 5 now and our next trip is in June and when I broke the news about Splash being closed for this year's trip, he was super disappointed. Obviously this approach will NOT be appropriate for all children; and you'll know your own littles well enough to know whether or not they'll be able to handle these types of things, but I happen to have quite an adventurous tiny human.
Naps were our saving grace. Thankfully, the hottest part of the day happens to fall during a lovely time to go back to the resort and take an afternoon nap. After 2-3 hours of relaxing, he was ready to conquer the world again (ADHD 3 y/o- need I say more?) and we would head back to the park for more fun.
Walmart and Target are super close to WDW and we always drive, so after we checked into the resort, we did a grocery run and stocked up on fixings for PB&J's, plenty of snacks and juice, water, chocolate milk everything toddlers run on.
That trip was before I met my now-wife and it was just Tiny Human and I. I worked two jobs as a single mom and I was SO BUSY, he went to daycare six days in a row some weeks; I know he and I both LOVED that uninterrupted week with just the two of us and I will never forget it. I'm a huge advocate for taking the tinies to Disney, honestly, it was one of the best trips I've ever done.