I'll expand a bit on what wooferhound is telling you.

A refrigerator/freezer does not create cold; it simply moves heat from one place to another, using energy to do so, some of which is wasted as heat. Therefore, the net "outflow" of the unit is heat, not cold, whether you have the door open or not.

Most freezers put their heat rejection coils on the outside of the freezer walls (not very efficient, but it's easier in a stand-alone relatively compact box, and electricity's still pretty cheap), usually in the front. If you put a box around that, you will have no joy at all because of the net outflow of heat.

As far as damaging the freezer goes, it depends. Most are designed with a maximum duty cycle in mind, but a more rugged one will be able to soldier on for quite a while full on. Since there is no reason to do this anyway (from paragraphs above), I recommend, uh, NO !