Cupcakes are just small versions of large cakes, which store well in a freezer and in fact can become more moist and dense after freezing. Often store purchased baked goods are frozen before they are sent to the store and decorated for purchase. Freezing does not harm the product as long as it is protected from freezer burn or absorbing odours from other foods. Proper preparation is the key.
Cool the baked cupcakes completely on a rack after they are removed from the oven. Remove them from the pan before cooling to allow the air to circulate around them.
Wrap each cupcake individually in a layer of cling film.
Stack the individually wrapped cupcakes in a freezer container and seal.
Store cupcakes in the freezer without a container by placing them inside a freezer Ziploc bag after wrapping them in the plastic. This method can allow more air to get to the cupcakes (air being the problem which damages frozen foods) so, if using this method, be sure the cling film on each cupcake is sealed well and that the Ziploc bag has excess air removed and is also sealed completely.
Stack cooled cupcakes in a freezer container in layers, placing waxed paper between the layers to prevent sticking. Close the container tightly. This method works well for very short term freezing.