Yes, you are absolutely allowed to bring a tumbler, such as a Yeti, Stanley, or Tervis, into the Disney theme parks. In fact, bringing a high-quality insulated tumbler is one of the most recommended "pro-tips" for staying hydrated in the intense Florida or California heat. There are only two main rules to keep in mind: first, the tumbler cannot be made of glass, as glass containers are strictly prohibited for safety reasons (except for small baby food jars). Second, you cannot bring "loose ice" inside the tumbler if it's in a cooler; however, having ice inside your drink in the tumbler is perfectly fine. A major benefit of bringing your own tumbler is that you can take advantage of the free ice water available at every "Quick Service" food location. Instead of drinking out of a small, flimsy paper cup, you can pour the water into your insulated tumbler to keep it ice-cold for hours. You can also bring your own coffee or tea in a tumbler to enjoy while waiting for the morning "rope drop." Just be prepared to place it in a bin or hold it securely during high-intensity rides, as most roller coasters do not have cup holders and will require you to stow the tumbler in a bag at your feet.