Like everyone has said, it 100% depends on the child. I took one niece just before 3 and the dark in Peter Pan scared her. My other niece (2 years old) BEGS to go on Snow White, it's her favorite (and my sister hates it!)...and one time we had a 5year old in front of us who was completely in tears after the ride while my niece is saying one more, one more.
Try a short dark ride, Peter Pan is a good option since it's short and just dark, not scary, or even Ariel, as that has dark segments but many familiar and happy sciences. If they do fine with that, HM will probably be okay, stretching room with the screams does tend to be the biggest trigger for fears, and at that point you could probably back out and not do the actual ride if it didn't go over well