According to the U.S. Department of Health Human Services' FoodSafety.gov, one can freeze a spiral ham. It recommends that frozen spiral hams be thawed and consumed within one to two months.
FoodSafety.gov recommends the same safe period for frozen leftovers of hams cooked at home. A GlobalPost article on spiral ham recommends careful handling and care of the spiral ham. The article suggests that spiral ham be placed in the refrigerator within a short amount of time from purchase. In accordance with the federal food safety information, the spiral ham should be good for up to five days when refrigerated and can be transferred into the freezer at any point during that time.