(A) Badgers are versatile and highly successful foragers and hunters, but I?ve never come across them climbing trees.
However, there are many records of them clambering a short way up tree trunks, helped by their powerful front legs and strong claws. They are also surprisingly agile, but their tree-climbing is restricted to lower levels.
If your feeder is only 3ft off the ground, it is certainly vulnerable to a hungry badger, and these animals are notoriously fond of peanuts. Once a badger has found a reliable source of food it is liable to make repeated return visits. The answer is to hang the feeder higher.