Bambi is a great movie for small children because the music is calming and the scenes are generally very soothing. Not a lot of fast action paced scenes that can make your kids hyper.
Sure there is a somewhat political message. But I doubt any child has seen that :)
The hardest thing to deal with is the question "where did Bambi's mother go?" If there is any hesitation to watch this movie with small children it is in regards to that potential question arising. Personally, I've not found it a big issue with my child.