Does putting batteries in the fridge keep them fresh?

When left unused, some batteries discharge quickly and some do not. This is true of both single use batteries and rechargeable batteries.

Discharge is a chemical reaction and chemical reactions are slower at lower temperatures. Refrigerated batteries are stored at a lower temperature, so some types of batteries will keep their charge better if stored in a refrigerator.

In addition to the chemical reactions that provide the voltage for battery function, there can be other reactions with the atmosphere that deteriorate the chemical composition of the battery. This can depend very much on the manufacture of the battery. If the battery is well made, then extraneous chemical reactions to battery materials from the air will be minimized by a well designed casing.

While there does not seem to be much careful data on the subject, there are at least some reasons to support a benefit from refrigeration. Even so, variations in manufacturers is likely to have a significant effect as well.