Everyone's really covered it, but just to add my two cents... I took a three-year-old who was barely 40 inches on everything our first trip, and she loved it all. However, she has one of those fearless personalities. My older dd, who was five at the time, was much more skittish. She went on everything, but needed encouragement and hand-holding to get through it. Even on our last trip when they were seven and five, my younger went on everything with her hands in the air, including ToT and Space Mnt. while my older was holding on for dear life!
Also, I don't think Screamin and Haunted Mansion are really comparable. Haunted Mansion is visually intimidating with scary stuff, while Soarin is a sweet, simple ride with no scary stuff. I'd say Screamin will not be a problem at all.