Donuts can be put in the fridge, but it often isn't the best method for keeping them fresh. Here are some reasons why:
Staling: Refrigeration can accelerate the process of staling, which is when bread-like products become tough and lose their moisture. This is due to the retrogradation of the starch in the doughnut. This means that the starch molecules realign themselves in a way that causes the doughnut to harden and lose its fresh-baked texture.
Drying Out: Refrigerators are designed to remove humidity, which helps to preserve certain foods. But for doughnuts and other baked goods, this dry environment can make them become dry and stale faster.
Flavor Loss: The cool temperature of a fridge can mute the flavors in a doughnut. You might not get the full sweetness and richness of the doughnut unless it's at room temperature.
If you have a surplus of doughnuts and can't eat them within a day or so (when they're usually at their best), freezing them might be a better option than refrigerating. When you're ready to eat one, let it thaw at room temperature or heat it up slightly in the microwave to revive the texture. However, it's important to note that not all doughnuts freeze well. Those covered in glaze or filled with cream or jelly can lose texture and flavor in the freezer. As a general rule, simpler doughnuts, like plain cake or yeast varieties, freeze better.
In any case, doughnuts are best when they're as fresh as possible.