Deer may be hung from the head or hind quarters.  The U.S. Department of Agriculture  recommends when hanging beef that it be hung by the hind quarters as this enables blood to drain from the choice hindquarters.  If you are taking the head as a trophy or skinning the animal you should hang from the hind quarters.  If however you are hanging the animal outside with the hide on it should be hung from the head.  This keeps moisture, rain or snow from trapping in the upturned hair.