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Assuming you mean "꿀떡" dessert and not some other type of Korean honey ricecake...

No idea if your fridge is changing the taste, but hope to help you on the texture issue.

For future reference, temperatures affect cooked rice and cooked rice flour products a great deal, as you've just discovered. This is why rice cookers that both cook and then keep rice warm are such a blessing -- As anyone who's taken home leftovers of white rice and stuck it in the fridge knows, it's never the same again.

꿀떡 should be eaten at room temperature. You probably can't get them back to exactly how they were. I might try to gently, slowly, steam them or put them in a slow slow cooker (like a closed rice cooker on warm setting) for a while, until they're warm and softer on the outside but haven't yet become hot in the filling.

You could also try to eat them after microwaving about 10 seconds, or you could roast them over a hot fire so they char slightly on the outside, according to this page: http://chowhound.chow.com/topics/640871

Many cultures foods are not able to be refrigerated the way Americans reflexively store everything in the low-temperature kitchen fridge (settings are kept so low to prevent molding and bacteria) -- instead, such foods are meant to be consumed within a day or two after purchase, and the only storage needed is a somewhat cool location.