Yes you can keep your batteries in the refrigerator especially if you are not using them right away.
When batteries are kept cold in the refrigerator the batteries usually last a lot longer and have a longer shelf life than batteries left out at room temperature.
Batteries that are left out at room temperature lose between 1 and 2 percent of the batteries charge per year and in very hot rooms or very hot temperatures such as 100 F or above the batteries can lose around 3 to 4 percent of their charge per year.
So by keeping the batteries cold in the refrigerator they will last longer.
I've tried it myself as an experiment because I heard about it on the radio before and I was not sure if it was gonna work.
So I purposely left a few batteries out at room temperature and then put a few batteries in the refrigerator and then checked the charge throughout the year after 6 months.
The batteries in the refrigerator had more charge in them than the batteries left out at room temperature so yes keeping the batteries in the refrigerator does work.
However that seems impossible since car batteries tend to lose their charge in cold weather but for some reason regular batteries we use in flashlights, remotes etc last longer in the refrigerator.
But I usually use my batteries well before they have a chance to go bad so I don't actually store any in the refrigerator except for that experiment.