I've never had a problem and this is what I typically take in with me:
Smuckers uncrustables for the kids (frozen so then they thaw while there)
trail mix
crackers (wheat thins, or peanut butter crackers)
cookies
fruit snacks
granola bars
water bottles
Everything is in an individual snack size, so I don't think they care. I wouldn't try to bring in a cooler, or a full lunch. I doubt they'd like that.
Like I said, after eating a large breakfast at the hotel, that's enough to tide us over during lunch, so then all we need to buy in the park is dinner.
ETA: I've heard that Sea World and the Zoo is much more picky about what people bring in because of the animals and things getting into their cages. Not sure if that's true, but that's what I was told.