Bring a coffee: food and beverages are not discouraged
Although you probably cannot have a picnic lunch in the middle of the Tropical Dome, you can certainly bring snacks and beverages or even a full lunch into the Domes. There are several seating areas inside between the domes with tables and chairs where many people eat a snack or lunch. They do sell wine and beer ($4.50) and cookies ($3.00) as you enter the domes and have a beverage and ice cream machine once inside. I could not find any coffee however, so stop on your way there if needed!