Is the hole in the back or the side? If in the side you did not damage the cooling. If in the back you possibly damaged the cooling but it's highly unlikely. Well that is unless you hit the rack with a hammer or something to get it to go in. The easy check is to open the outside panel of the refrigerator.
If you smell ammonia or see that everything is dusted with yellow powder you have a problem. If no smell and no powder you are probably okay.
If no smell or powder I would pull the wire out. Then get a tube of some caulking (whatever you have on hand) and squeeze it into the hole. Take a wet finger and smooth the caulking out so it is just neatly filling the hole but not making a big glob inside the refrigerator. Let the caulking dry and don't give it another thought.
