We didn't take ours to WDW until he was 3. At ages 3 through 5, we followed "his schedule". Which is to say, we absolutely honored the normal afternoon nap that he took every day back home. So we would go to the parks at rope drop and stay the whole morning. Eat a nice table lunch somewhere, do a few more things, then leave the park at 2 for the quiet of our hotel room or DVC unit (we always drive, so we could get back quickly). Nap for a couple hours, then go back out for 5-6 hours in the evening, and have him back in bed by 10, which was 2 hours later than his normal time, but got him to the evening "hurraydes" as he called them. Most importantly, he was happy and rested for both halves of our park days.
Honestly that 2 hour afternoon nap helped us parents too - getting out of the heat, noise and crowds for a little while kind of refreshed us to dive back in for a second round of the day, which was often in a different park than the first half. If I didn't sleep I read a book.
Vacations with exhausted, whiny, screaming, crying kids (and usually that means the parents are screaming back at them) are not really vacations, they're endurance tests. Both for the kids and those around them.
One of the few sad parts of being at Disney for me is that invarably we'll run across those families in the middle of giant meltdowns, often because people are overtired and overstimulated.
That said, it really depends on your kids, and only you know how far they can go. Do they nap now? If they don't nap now, maybe consider taking a blanket with you and just having some "quiet time" in the park midafternoon. We still do this even though we have no little kids anymore! Find a quiet patch of grass and rest. I took a nap in Epcot last New Years... lol.
If they do regular naps now, and you let them skip it, how are they the rest of the day? Are they functional or so overtired they won't behave? Would it be okay for you to manage them while they are overtired, or would it stress you out? What time do they go to bed in the evening? Would an afternoon nap help them stay awake and happy until 10 or so, so you can see the midevening parades and fireworks? All stuff to think about.