my dd was exactly like this on our first trip when she was 3 1/2. actually she would have been ok, but we took her on teh Cat in the Hat (at IOA) for her first ride, it spooked her, and it took a long time to get her confidence back.
My suggestion would be to start with It's a Small World - there is nothing at all scary on this ride, Dumbo is very safe too, although the lines can be long. Pooh is mostly ok, but dd was a little nervous of the heffalump scene. But, by asking the CM at the entrance to each ride, what would happen, was anything scary, etc, and pushing the CM to really tell us if there was a scary scene, my dd was quite happy to ride lots of things by the end of our trip.
Work your way up slowly, there is no need to try and do everything the first day, make sure you have a good guidebook and are aware of what happens on each ride - a mistake like mine with the Cat in the Hat can shake them for a long time.
I would not even touch Snow White, it's a stupid ride in that it scares the little ones, but is too tame for the older ones. Likewise, I wouldn't go near Haunted Mansion - we can't even walk past it without my dd pointing out that she is not going on that thing.
She does like Pirates now, but we didn't do it on our first trip, but worked up to it.
Another thing to consider is that the rides at your local amusement park are probably quite different to the WDW rides - more of the Disney rides are about sitting in a car and watching a show, for example, It's a Small World I would describe to him as a boat trip rather than a ride. And I have to tell you, that I had to strongly encourage my dd to go on Its A Small World, and the grin on her face when she realised it wasn't scary at all, and she actually quite liked it was worth the price of the whole holiday!
Mind you, we had to ride it about 10 times, which is quite a price to pay....
Bev