This could be a rather interesting question..but I do believe you are talking about a whoopie pie. They are a rather moist cake did you cool completely before freezing? It just might be a bit of excess moisture.
I would doubt that it will effect the taste at all. Just tell people to eat them fast and lick their fingers!
I am also assuming that you are refering to the cake itself and not the filling, is this correct?
Some of the filling recipes that I have seen call for marshmallow, others call for whipped eggwhites. I don't know how either one of those would hold up to freezing.
The filling I make is made with a milk and flour mixture that is cooked, cooled then whipped into butter and sugar. It freezes well.
By the way there are MANY parts of the country that have no idea what a whoopie pie is! I brought some back to the midwest from Maine and no one knew what they were.