Yes, you can bring some PB&J, carrots, raisins. Turkey and Cheese sandwiches are OK too. Jelly beans are OK.
What you can't bring in: A whole rotiserrie turkey with mashed potatoes, green bean casserole plus a whole side of ham and some raw steaks to go along with your grill. Now that's a no-no.
Bring some snacks, they're not going to arrest you, kick you out of your resort, and escort you back to the airplane!
As fas as my must pack items:
moleskin
ziploc bags
cream antiperspirant to prevent chafing (for DH) and for keeping feet dry
a bandana - it doubles as a little towel to dry off after Splash mountain, to mark your stroller, a mini blankie for DS, to cover up DS's face when he's scared on parts of It's Tough to be a Bug, to wipe camera lenses, to wipe off sweat, etc.
extra batteries and battery charger.