Universal Orlando allows almost all food/drinks through security checkpoint *before 5pm* during HHN (and anytime during non-HHN nights). If you're doing stay and scream then you'd be fine since you're arriving before 5pm.
Notes:
No alcoholic beverages - they'll check all your canned beverages to make sure they're non-alcoholic so be ready to show them.
No glass containers (so for example, no Starbucks glass coffees).
No large hard coolers. I bring a larger soft-cooler backpack loaded with food, canned sodas, and ice packs.
After 5pm: they're strict about not allowing any drinks through. They're less strict about not allowing food through but I think it depends on what security feels like allowing on that night.
Quick tip: you can bring a container with ice cubes (like a large plastic refillable water bottle), and refill the ice from the soda machines when the ice starts melting later in the night. This'll keep your stuff cool all night.