We have both in our house, though I didn't even realize we had the book until I saw it on E's shelf the other day. A neighbor gave us a ton of books from his kids last year, many for older chidren and this was from that stack. We haven't read it yet, so at this time neither of my children are familiar with the story. I will read it to them, though, eventually.
When I consider how they will react to the characters' depiction, honestly, I'm more concerned about the figure of Snow White than the seven dwarfs. These seven white-bearded little men with one-dimensional personalities who work in a mine and keep house as if they were children have little in common with my daughter. Yes, they conform to Germanic mythology's mountain-dwelling, mining dwarfs. Yes, they each personify a particular human weaknesses or foible. However, their childlike bickering and inability to care for themselves strike me as more insulting to men in general rather than little people specifically.
As a young girl, Belalu is more likely to identify with Snow White than the other characters. They even have similar coloring- dark hair and eyes, pale skin... But I hope that is where the identification ends. Snow White is a simpering, gullible BORing young woman whose best traits are being "the fairest in the land" and a good housekeeper to a bunch of ungrateful bachelors. Her life continuously depends on the kindness and charity of the men she stumbles upon, from the hunter who let her escape death, the dwarfs who house her (in exchange for maid service), to the prince who rescues her and takes her away to live happily ever after in a castle. (I hope there she at least has some help with the domestic upkeep.)
If I were to be afraid of her taking away a negative message or influence from this book, it would definitely be in the title character. However, I don't think my attempts to limit her exposure to Snow White or any of the other fairy tale princesses will do her any favors. Rather, I plan on talking to both of my children about the books we read and movies we watch, so they can think critically about the material rather than accept it at face value.