Here's what the authors have to say about it:
Amazing that the first movies parents took their tots to in the 30s and 40s were the early Disney features. Snow White and the Seven Dwarfs, Pinocchio, Dumbo all exploited childhood traumas. Parents disappear or die; stepmothers plot the murder of their charges; a boy skips school and turns into a donkey. Kids were so frightened by these films that they wet themselves in terror. Bambi, directed by David Hand, has a primal shock that still haunts oldsters who saw it 40, 50, 65 years ago.
I dunno. I just can't see that as being a valid point on a variety of levels. First and foremost, Bambi was never meant to be a horror movie. Second, don't you think the kids from back then would have been even more freaked out if we took a bootleg copy of SAW IV and chucked it through the time machine and ran a screening for them?
Personally, I don't recall anything at all terrifying about Bambi. Still, to this date I've never seen the Black Cauldron and I remember stories when I was a kid that the theatrical version had been pulled from the Disney lineup, never again to make it to theaters, because it terrified kids. I think that changed just recently but it's not like I go and see many movies, much less ones aimed at kids. Hell, I can't even find people willing to see The Nightmare Before Christmas 3D and that kicks arse. Alas, woe is me.