My dd and I went to WDW last August, and the Brita bottles were a lifesaver. I was an annoying Guest, I'm sure, because I kept filling our bottle with the ice chips they use to keep the spray bottle/fans cold! I figured, hey the filter will screen out most yucky stuff, and as the ice melts, we'll always have cold water!
I got a few borderline dirty looks in EPCOT, but no one told me to stop. It was in the mid-upper 90's on that particular day, which is probably why I was allowed to continue. We got a great deal on our spray fans, by the way, at Wal-Mart. They were about $5, compared to $18 at the parks.
Have a great trip!
-Sarah