I think you are right to be concerned with bears in the woods. From personal experience I can talk about them raiding and taking the best steaks, along with a bag of ice. Why they wanted the ice, who knows, but the bag was no where to be found. Maybe they wanted to keep the meat cold.

And it was a four legged thief for sure. They (it) left tooth marks in the cooler and the paw prints on the table.
So after that, my hunting buddy and I moved the coolers to the trucks when we left camp and at night as we did not have a hard side CT or TT. We should have known better about the cooler being left out.

We have been at this for many years. Just forgot about it that night. And I guess we never thought about the possibility of a bear trying to rip a the doors and windows of the trucks. There is always something to think about when you venture away from home.
For my CT, I plan on having a large cooler in the back (CT w/barn doors) for reserve cooling and a smaller one inside the CT for day-to-day use. I will probably use block ice for the larger one to get the maximum cooling life out of it.