yes you ARE allowed to bring in food.
prepared sandwiches are permitted (bringing a jar of peanut butter, a jar of jelly, a loaf of bread, and a knife would not be permitted as its not pre prepared)
you may also bring snacks such as goldfish, granola bars, cookies, potato chips...
and you can also bring drinks such as juice boxes, bottled water, or soda.
you can bring it in a backpack or a small soft sided cooler.
you will have to go through the bag check and they will look in your bag but there is no need to be worried about letting them see that you have food and drinks since it is allowed.
the only exceptions are that you cannot bring in glass unless is baby related such as a glass baby bottle or jar of baby food and you cannot bring alcohol into the parks.