I have a summer cottage in north east Ohio that has no insulation. It is generally going to be used in the summer (Apr - Oct). I have removed the paneling from the inside of the exterior walls. Should I insulate or could it cause more issues , such as mold? I want to use dry wall on the interior side. Would I insulate and use a vapor retardant instead of a moister barrier?

The purpose of insulation is to keep hot and cold air separated. There's a way to keep the hot air outside is to create an air pocket. You can create a space where an air pocket acts as a buffer between the outside and inside. That air pocket will absorb much of the outside cold or hot and keep the inside more livable.