Although I like Snow White's intelligence in terms of knowing she should find a safe place to sleep (although I think that was less for safety and more just... needing a place to stay) and how she knows the dwarfs are lying about washing their hands, on the whole Snow White doesn't really demonstrate any real intelligence in any facet.

Common sense and resourcefulness. even though she had to rely on the animals for help, it's still being resourceful. And then doing the logical thing of offering her talent at housekeeping in exchange for shelter and protection instead of doing something that just doesn't make much sense to do, like trying to help in the mines (where she'd probably just get in the way) or sit around and do nothing to repay the dwarfs' kindness with.

Yeah, I guess.

Cleverness and some common sense.