Hi asukeith!
I can tell you our experience bringing a backpack in last summer.
It was a standard-size Land's End backpack and it worked out great for carrying the day's necessities, particularly diaper supplies and extra clothes for our baby and toddler. Security looked in every pocket of the backpack before we entered the park. They were looking for dangerous items, not snacks--we brought a few snacks (granola bars, a couple of juice boxes) and that was not a problem. I believe Disney's official policy is no outside food or drink, and we tried to respect that by bringing just a small stash of snacks for the kids, but to my knowledge Disney does not enforce the rule. As far as I know there is no restriction on the size of the backpack, though I can't imagine you would want to bring a huge one simply because it would be hard to take it on the rides. We found it very easy to take our standard-size backpack on all the rides--I would just loop it carefully around my leg so it wouldn't fall out and so I wouldn't forget it.
Have a great trip!